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Carr G.S. — Formulas and Theorems in Pure Mathematics
Carr G.S. — Formulas and Theorems in Pure Mathematics



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Название: Formulas and Theorems in Pure Mathematics

Автор: Carr G.S.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1970

Количество страниц: 988

Добавлена в каталог: 07.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Integrals or Integration, indefinite circular functions, $sin x, sin^{-1}x, &c.$      1938—1949
Integrals or Integration, indefinite circular functions, $sin^{n}x, &c.$      1954—1957
Integrals or Integration, indefinite circular functions, $\frac{1}{(a+bcos x)^{n}}$      1958 Me.80
Integrals or Integration, indefinite circular functions, $\frac{1}{a+bcos x}$      1951 J.9
Integrals or Integration, indefinite circular functions, $\frac{F(cos x)}{(a_{1}+b_{1}cos x)(a_{2}+b_{2}cos x)...&c.}$      1996
Integrals or Integration, indefinite circular functions, $\frac{F(sin x, cos x)}{acos x+bsin x+c}$      1994—1997 A.12 J.19 32
Integrals or Integration, indefinite circular functions, $\frac{sin kx}{x\, or\, sin x}f(x)$ (Fourier)      2726—2742 A.38
Integrals or Integration, indefinite circular functions, $\frac{sin^{n}x}{x^{m}}$      A.17
Integrals or Integration, indefinite circular functions, $\frac{sin^{n}x}{x^{m}}$ with m=1      G.7
Integrals or Integration, indefinite circular functions, $\frac{sin^{n}\phi}{(1-ksin\phi)\surd(1-k^{2}cos^{2}\phi)}$      A.11
Integrals or Integration, indefinite circular functions, $\surd\{1-k^{2}sin^{2}\frac{1}{2}(a+x)sin^{2}\frac{1}{2}(a-x)\}$      J.39
Integrals or Integration, indefinite circular functions, a function of sine or cosine in a rapidly converging series, and successive integration of it      J.4 15
Integrals or Integration, indefinite circular functions, binom. funcs. of sin and cos      1982—1992
Integrals or Integration, indefinite circular functions, ditto of tangent      1983 1991
Integrals or Integration, indefinite circular functions, limits 0 to $\frac{\pi}{2}$, $cos^{p-n-1}x sin^{n-1}x{sin \atop cos}px$; and $sin^{p-2}x sin px$      2585—2588
Integrals or Integration, indefinite circular functions, limits 0 to $\frac{\pi}{2}$, $cos^{p}x{sin \atop cos}nx$      2481 2484—2492 L.43
Integrals or Integration, indefinite circular functions, limits 0 to $\frac{\pi}{2}$, $sin^{n}x cos^{p}x$      2459—2465
Integrals or Integration, indefinite circular functions, limits 0 to $\frac{\pi}{2}$, $sin^{n}x$      2453—2455 2458 2472 E.29
Integrals or Integration, indefinite circular functions, limits 0 to $\frac{\pi}{2}$, $sin^{n}x, n=\frac{1}{2}$      E.28
Integrals or Integration, indefinite circular functions, limits 0 to $\frac{\pi}{2}$, $tan^{2m-1}x$      2457
Integrals or Integration, indefinite circular functions, limits 0 to $\frac{\pi}{2}$, $x cos^{n-2}x sin nx$      2494
Integrals or Integration, indefinite circular functions, limits 0 to $\frac{\pi}{2}$, $x cot ax$      A.34 No.19
Integrals or Integration, indefinite circular functions, limits 0 to $\frac{\pi}{2}$, $x tan\frac{1}{2}\pi(1-bx)$      5340
Integrals or Integration, indefinite circular functions, limits 0 to $\frac{\pi}{2}$, $\frac{1}{a^{2}cos^{2}x+b^{2}sin^{2}x}$ and similar      2496—2501 2344
Integrals or Integration, indefinite circular functions, limits 0 to $\frac{\pi}{2}$, $\frac{cos^{n-1}x sin ux}{sin x}=\frac{\pi}{2}$ and similar      A.59
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $x^{\pm m}{sin \atop cos}bx$      2579—2581
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{1-cos^{m}x}{x^{2}}$      Z.7 8
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{1\, or\, x sin cx}{(1+x^{2})(1-2a cos cx+a^{2})}$      2630—2632
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{1}{x^{2}}tan^{-1}\frac{x}{a}tan^{-1}\frac{x}{b}$      2504
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{cos 2ax sin^{p}x}{x^{m}}$      2722—2725
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{cos bx}{x+a}$, also $\int^{x}_{\infty}\frac{cos x}{x}dx$      A.10
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{cos qx-cos px}{x\, or\, x^{2}}$      2513—2515
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{cos rx}{(a^{2}+x^{2})^{n}}$      L.40 Q.18
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{cos rx}{a^{2}+x^{2}}$      2573 A.10 11 59 J.33 Me.72 76 Z.7 8
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{cos x}{\surd x}$, $cos x^{2}$, $cos(ax)^{2}$      2507—2509 Q.12 2602
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{sin ax sin bx}{x}$ and similar      2514—2522
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{sin ax}{(1+x^{2})sin bx}$ and related integrals      Ac.7
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{sin rx}{x}$      2572 L.49 Z.7 8
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{sin^{n}x}{x^{p}}$      2510 A.30 E.26 Z.5
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{sin^{n}x}{x^{p}}$, n=2 and 3      2511—2512
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{tan^{-1}ax-tan^{-1}bx}{x}$      2505
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{tan^{-1}ax}{x(1+x^{2})}$      2503
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{x sin rx}{a^{2}+x^{2}}$      2575 A.10 J.33
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{\phi(n){sin \atop cos}rx}{a^{2}+x^{2}}$      A.11
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{\phi(n){sin \atop cos}rx}{a^{2}+x^{2}}$ with $\phi(x)=tan^{-1}cx$      A.11
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{\phi(n){sin \atop cos}rx}{a^{2}+x^{2}}$ with $\phi(x)=x^{m}$      L.46
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{\phi(sin ax, cos bx)}{x}$      J.23 25
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\frac{{sin \atop cos}(ax)^{2}}{a^{2}}+x^{2}$ and similar      Z.13
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, $\phi(sin ax, cos bx)$, reduction of      J.15
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, ${sin \atop cos}x^{n}$      Me.72
Integrals or Integration, indefinite circular functions, limits 0 to $\infty$, ${sin \choose cos}^{2}x$      Q.13
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $cos n(x-a sin x)$      L.41
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $cos n(x-a sin x)$, $0\, to\, \pi$      C.39
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $cos(a+nx)cos(b+px)cos(c+qx)$      C.54
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $sin nx{sin \atop cos}px$      2467—2469
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $sin^{2n}x d_{nx}f(cos x)$      2495
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $sin^{n}x cos^{p}x$      2459
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $xF(sin x cos x)$      JP.27
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $\frac{sin^{2n}x\, or\, cos px}{(1-2a cos x+a^{2})^{n}}$      Q.11 LM.11
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $\frac{sin^{2n}x\, or\, cos px}{(1-2a cos x+a^{2})^{n}}$, n=1      L.74
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $\frac{x sin x\, or\, sin x sin rx\, or\, cos rx}{1-2a cos x+a^{2}}$      2623—2629
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $\frac{x sin x}{1+a^{2}cos^{2}x}$      Pr.25
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, $\frac{x sin x}{1+a^{2}cos^{2}x}$ with a=1      2506 Q.11
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, ${sin \choose cos}^{p}x{sin \atop cos}nx$      2474—2482 2493
Integrals or Integration, indefinite circular functions, limits 0 to $\pi$, about 250 integrals with limits chiefly from 0 to $\pi$, some from 0 to $\infty$      Pr.25 26 27 29 30 31 32 33
Integrals or Integration, indefinite circular functions, other limits, $\int^{1}_{0}\frac{tan^{-1}ax dx}{x\surd(1-x^{2})}$      2502
Integrals or Integration, indefinite circular functions, other limits, $\int^{1}_{0}\frac{tan^{-1}x}{1+x}dx$, deduced from (2416)      L.69
Integrals or Integration, indefinite circular functions, other limits, $\int^{2\pi}_{0}\frac{dx}{a+b cos x+c sin x}$, lim 0 to $2\pi$      A.55
Integrals or Integration, indefinite circular functions, other limits, $\int^{\infty}_{-\infty}\frac{F(x)}{x^{n}}dx$, where F(x) is a rational integral circular function      CM.3
Integrals or Integration, indefinite circular functions, other limits, sine-integral, &c.      see "Functions"
Integrals or Integration, indefinite circular functions, products and quotients of sine and cosine and their powers      1959—1980 2066—2070 A.49
Integrals or Integration, indefinite circular-exponential functions, $(e^{ix}sin x)^{n-1}$      L.74
Integrals or Integration, indefinite circular-exponential functions, $e^{ax}{sin \choose cos}^{n}bx$      1999
Integrals or Integration, indefinite circular-exponential functions, $e^{x}sin^{n}x cos^{n}x$      2000
Integrals or Integration, indefinite circular-exponential functions, limits 0 to $\infty$, $e exp \left\{-\left(x^{2}+\frac{a^{2}}{x^{2}}\right)cos\theta\right\}\times &c.$      2606 Q.12
Integrals or Integration, indefinite circular-exponential functions, limits 0 to $\infty$, $e exp(-a^{2}x^{2}){cos \atop cosh}2bx$, and similar      2614—2618 Z.1 10
Integrals or Integration, indefinite circular-exponential functions, limits 0 to $\infty$, $e^{-ax}sin bx$      2583
Integrals or Integration, indefinite circular-exponential functions, limits 0 to $\infty$, $e^{-ax}sin bx$, 0 to 1      Mem.30
Integrals or Integration, indefinite circular-exponential functions, limits 0 to $\infty$, $e^{-ax}x^{m}{sin \atop cos}bx$      2577 2589 J.33 Z.7
Integrals or Integration, indefinite circular-exponential functions, limits 0 to $\infty$, $e^{-ax}{sin \choose cos}^{m}x$      2608—2611 A.7
Integrals or Integration, indefinite circular-exponential functions, limits 0 to $\infty$, $e^{-kx}cos mx sin^{n}x$      2717—2720
Integrals or Integration, indefinite circular-exponential functions, limits 0 to $\infty$, $\frac{cos x-e^{-ax}}{x}$      2619
Integrals or Integration, indefinite circular-exponential functions, limits 0 to $\infty$, $\frac{e^{-ax}sin rx}{x}$      2571 2591
Integrals or Integration, indefinite circular-exponential functions, limits 0 to $\infty$, $\frac{e^{ax}+e^{-ax}}{e^{\pi x}+e^{-\pi x}}sin mx, &c.$      2593—2600
Integrals or Integration, indefinite circular-exponential functions, limits 0 to $\infty$, with limits $-\frac{\pi}{2}$ to $\frac{\pi}{2}$      2612
Integrals or Integration, indefinite exponential functions, $e exp(\frac{1}{2}x^{2})$      E.34
Integrals or Integration, indefinite exponential functions, $e^{x}$, $a^{x}$      1924
Integrals or Integration, indefinite exponential functions, $e^{x}\{\phi(x)+\phi^{'}(x)\}$      1998
Integrals or Integration, indefinite exponential functions, $x^{m+nx}$      2004
Integrals or Integration, indefinite exponential functions, $\frac{e exp(-x^{2})}{\surd(a+bx^{2})}$, or the same $\times x^{2}$ or $\div(c+dx^{2})$      L.52
Integrals or Integration, indefinite exponential functions, limits 0 to $\infty$, $e exp(-kx^{2})$      2425
Integrals or Integration, indefinite exponential functions, limits 0 to $\infty$, $e exp(-kx^{2})$, evaluation by a continued fraction      J.12
Integrals or Integration, indefinite exponential functions, limits 0 to $\infty$, $e exp(-x^{2}-\frac{a^{2}}{x^{2}})$      2604—2605 L.56
Integrals or Integration, indefinite exponential functions, limits 0 to $\infty$, $e exp(ax^{n})$. $Ei(\pm ax^{n})$      Q.18
Integrals or Integration, indefinite exponential functions, limits 0 to $\infty$, $e^{-ax}e^{i(x^{2}+bx)}$      Mel.2
Integrals or Integration, indefinite exponential functions, limits 0 to $\infty$, $e^{-kx}x^{n}$      2284—2291 see
Integrals or Integration, indefinite exponential functions, limits 0 to $\infty$, $\frac{e^{-nx}}{1+x^{2}}$      Z.6
Integrals or Integration, indefinite exponential functions, limits 0 to $\infty$, $\frac{e^{-nx}}{1+x^{2}}$, ditto $\times x^{m}$      L.46
Integrals or Integration, indefinite exponential functions, limits 0 to $\infty$, $\frac{e^{-nx}}{x^{2}-a^{2}}$ and the same $\times x$      A.10
Integrals or Integration, indefinite exponential functions, limits 0 to $\infty$, other forms      2426—2431 2595 2598 2601
Integrals or Integration, indefinite exponential functions, other limits, $\int^{2\pi}_{0a}F(re^{\phi i})e^{-n\phi i}$      A.15
Integrals or Integration, indefinite exponential functions, other limits, $\int^{\infty}_{\xi}e exp(-x^{2})[\equiv Erfc\xi(Glaisher)]$      Me.76
Integrals or Integration, indefinite exponential functions, other limits, $\int^{\xi}_{0}e^{-kx}F(x)dx$      C.77
Integrals or Integration, indefinite exponential functions, other limits, $\int^{\xi}_{0}x^{2n}e exp(-x^{2}-\frac{a^{2}}{x^{2}})$      C.12
Integrals or Integration, indefinite exponential functions, other limits, expon-integral      see "Functions"
Integrals or Integration, indefinite exponential functions, X being a rational integrate function of x: $e exp(-x^{2})$      Q.1
Integrals or Integration, indefinite exponential functions, X being a rational integrate function of x: $e^{X}$      Mem.83
Integrals or Integration, indefinite exponential functions, X being a rational integrate function of x: $e^{x}X$      J.13
Integrals or Integration, indefinite logarithmic functions, $x^{m}(log x)^{\pm n}$      2003—2006
Integrals or Integration, indefinite logarithmic functions, $x^{m}log(1+x), &c.$      A.39
Integrals or Integration, indefinite logarithmic functions, $\frac{x^{l}(log x)^{m}}{x\pm 1}$ and a similar form      2030—2032
Integrals or Integration, indefinite logarithmic functions, $\frac{x^{m}log x}{(1-x^{n})^{p}}$, type of several      Mem.18
Integrals or Integration, indefinite logarithmic functions, F(x)log x      G.12
Integrals or Integration, indefinite logarithmic functions, limits 0 to $\infty$      2423—2424
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, $log\frac{1}{x}$      2284
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, $x^{k}(log\frac{1}{x})^{n}$      2291
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, $\frac{1}{x}log\frac{1+x}{1-x}$      2403 L.73
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, $\frac{log x}{\surd(1-x^{2})}$      2636 Q.12
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, $\frac{log(1+x)}{1+x^{2}}$      2416 C.59 J.6 L.43 44
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, $\frac{x^{m-1}log x}{1+x^{m}}$, and many cases      J.34
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, $\frac{x^{m}(x-1)^{n}}{log x}$      Z.3
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, $\frac{x^{m}-1}{log x}$      A.37
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, about 130 expressions of the forms, $x^{m}(1-x^{n})^{p}(log x)^{2\, or\, 3}$, $x^{m}(1-x^{n})^{\frac{p}{q}} log x$, and $\frac{x^{m}(x^{nr}-1)}{x^{r}-1} log x$, with integral values of w, n, p, q, and r      A.40
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, about 280 expressions, nearly all comprised in the form $x^{m}(1-x^{n})^{\frac{p}{q}}(log x)^{t}$, with integral values of m, n, p, q, and t      A.40
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, about 540 expressions chiefly formed from $log(1\pm x)$ or $log(1\pm x_{n})$ or $log(1+x+x^{2})$ or $log(1+x^{2}+x^{4})$, joined to a single factor of the form $x^{m}$ or $(1\pm x^{m})$ or $\frac{1\pm x^{m}}{1\mp x^{m}}$ with integral values of m and n      A.39 40
Integrals or Integration, indefinite logarithmic functions, limits 0 to 1, involving log x or $log(1\pm x)$      2391—2403 2416—2422
Integrals or Integration, indefinite logarithmic functions, log x      1950
Integrals or Integration, indefinite logarithmic functions, other limits, $\frac{1}{x}log\frac{1+x}{1-x}$, limits 0 to $\surd 2-1$      2415
Integrals or Integration, indefinite logarithmic functions, other limits, $\frac{log(1-x)}{x}$      2408—2412 L.73 Z.1
Integrals or Integration, indefinite logarithmic functions, other limits, log-integral      see "Functions"
Integrals or Integration, inverse method      CM.4 CP.4 5 L.78
Integrals or Integration, involving elliptic functions      Pr.29 Q.19
Integrals or Integration, limits of      2233—2244 L.74 1903 1906 2233 2775
Integrals or Integration, miscellaneous theorems, $\int f(x)sin\omega\pi x d(log x)$      Mo.85
Integrals or Integration, miscellaneous theorems, $\int f(x)\phi(x)dx$      L.49
Integrals or Integration, miscellaneous theorems, $\int f(x-R)dx=\int f(y)dy$      CD.4
Integrals or Integration, miscellaneous theorems, $\int\frac{(x+p)(x+q)^{\theta}d\theta}{x^{m+1}(x+p+q)^{n+1}}, \theta\equiv pos\quad integer$      C.78
Integrals or Integration, miscellaneous theorems, $\int\frac{du}{uU\psi(u)}=log\psi(u)+C$      J.19
Integrals or Integration, miscellaneous theorems, $\int\phi(x)\{\Psi(x)\}^{\pm n}$      2001—2002
Integrals or Integration, miscellaneous theorems, $\int\Pi(x, y)dx$      J.61 Mo.61 Q.7
Integrals or Integration, miscellaneous theorems, $\int^{1}_{0}(u)_{n}du$      Z.25
Integrals or Integration, miscellaneous theorems, $\int^{1}_{0}(u+k)_{k+2}du=(-1)^{k}\int^{1}_{0}(u)_{k+2}du$      A.38
Integrals or Integration, miscellaneous theorems, $\int^{1}_{0}P_{m}(x)P_{n}(x)dx\quad(P_{m}x\equiv Legendre's\quad coeff.)$      Pr.23
Integrals or Integration, miscellaneous theorems, $\int^{1}_{0}uvdx{> \atop <}\int^{1}_{0}udx\int^{1}_{0}vdx$      AJ.7
Integrals or Integration, miscellaneous theorems, $\int^{b}_{a}f^{'}(x)=f(b)-f(a)$      1901—1903 A.16
Integrals or Integration, miscellaneous theorems, $\int^{b}_{a}\frac{\phi(ax)-\phi(bx)}{x^{n}}dx$      Me.81
Integrals or Integration, miscellaneous theorems, $\int^{b}_{a}\frac{\phi(ax)-\phi(bx)}{x^{n}}dx$, n=0      2700
Integrals or Integration, miscellaneous theorems, $\int^{\frac{\pi}{2}}_{0}\phi(sin 2x)cos x dx=\int^{\frac{\pi}{2}}_{0}\phi(cos^{2}x)cos x dx$      A.21 L.53
Integrals or Integration, miscellaneous theorems, $\int^{\infty}_{-\infty}F(x)dx$, approx. to      C.97
Integrals or Integration, miscellaneous theorems, $\int^{\infty}_{-\infty}\phi(x+\frac{1}{x})\frac{f(x)}{x}dx$, and similar      Me.75 76 77
Integrals or Integration, miscellaneous theorems, $\int^{\infty}_{0}\frac{f(\theta x)}{x^{r}}dx$ ($\theta$ of Taylor's th      LM.13
Integrals or Integration, miscellaneous theorems, $\int^{\infty}_{0}\frac{r}{r^{2}+x^{2}}\Phi{cos \atop sin}x\Psi{sin^{2} \atop cos^{2}}x$, trans. of      J.36
Integrals or Integration, miscellaneous theorems, formulae of Frullani, Poisson, Abel, Kummer, Cauchy, &c.      2700—2713
Integrals or Integration, miscellaneous theorems, if f(x+iy)=P+iQ, th      2710
Integrals or Integration, miscellaneous theorems, integrals deduced from z''+Pz'+Qz=0, and y''+(P+2R)y'+{Q+R(P+R)+R'} y=0      J.18
Integrals or Integration, multiplication of      Pr.23
Integrals or Integration, number of linear independent of 1st kind      An.82
Integrals or Integration, periods of      C.36 38 75 G.75 JP.27
Integrals or Integration, principal values of infinite definite      2240 A.68
Integrals or Integration, properties by elliptic coordinates      L.51
Integrals or Integration, quotient of two d.i of the form $\int dx dy...dz$      J.67
Integrals or Integration, reduction to elliptic functions      An.60 LM.12 Me.77 78
Integrals or Integration, residues of      JP.27
Integrals or Integration, Riemann's of first kind      An.79
Integrals or Integration, sine and cosine      G.6 M.11
Integrals or Integration, singular values of      A.11
Integrals or Integration, successive      2148 L.62
Integrals or Integration, successive, 2nd order      M.20 Z.11
Integrals or Integration, summation of      2250 J.47 JP.12 21
Integrals or Integration, tables of definite, by de Haan, B., note on      C.47
Integrals or Integration, theorems      L.48 P.55 Q.10 12
Integrals or Integration, transformation of      2245—2252 A.10 CM.4 J.f15 22 36 L.36 Mel.3 Q.1
Integrals or Integration, use of imaginaries in      M.14
Integrals or Integration, variation of arbitrary constant      2247 J.33
Integrals or Integration, whose derivatives involve explicit functions of the same variable      C.12
Integrals or Integration, whose values are algebraic      J.10 JP.14 L.38
Integrating factors of d.e      pp.468—471 3394
Integrator mechanical      5450
Intercalation      CM.3
Intercepts, to find      4115
Interest      296 296—301 N.48 61 64
Interest and insurance      A.26
Interpolating functions      C.11
Interpolation      3762 A.32 61 62 70 AJ.2 C.19 48 68 92 J.5 L.37 46 Me.78 N.59 76 Q.7 8
Interpolation and mechanical quadrature      3772 A.20
Interpolation and summation      I.11 12 14
Interpolation by a parabolic curve      2992 C.37
Interpolation by circular functions      N.85
Interpolation by cubic and quintic equations      C.25
Interpolation by method of least squares      C.37 Mem.59
Interpolation of algebraic functions, Abel's th      J.28
Interpolation of values from observation      Mel.2 tr Mem.59
Interpolation, Cauchy's method      A.2 C.37 L.53
Interpolation, formula for odd and even functions      C.99
Interpolation, formulae      J.2 C.99 Mo.65
Interpolation, formulae, Lagrange's      3768 J.1 84 N.57 61
Interpolation, formulae, Newton's      N.57 61 71
Interpolation, Stirling's series      Me.68
Interpolation, tables      I.11
Intersection of 2 conics      4916 CD.5 6 N.66
Intersection of 2 curves      4116 4133 CM.3 J.15 L.54
Intersection of 2 curves by rt. lines      Me.80
Intersection of 2 planes      5528
Intersection of 2 quadrics      C.62 N.68
Intersection of circles and spheres      L.38
Intersection of right line and conic      see "Right line"
Intersection of successive loci, ths      N.42
Intersection of surfaces      J.15 L.54
Intersection of surfaces by rt. lines      Me.80
Invariable line, plane, conic, and quadric      5856—5866
Invariants      1628 An.54 C.85 E.42 G.1 2 15 J.62 68 69 L.55 61 76 M.3 5 17 19 Me.81 N.58 59 69 70 P.82 Pr.7 Q.12 Z.22
Invariants and covariants of $f(x^{2}, y^{2})$ relative to linear transformation      G.17
Invariants of a bi-ternary quadric      J.57
Invariants of a binary quadric      M.3
Invariants of a binary quantic      1648 E.40 Me.79
Invariants of a binary quantic, of two      1650
Invariants of a binary quantic, table of irreducible      AJ.1
Invariants of a binary quartic      M.3 Q.10
Invariants of a conic      4417 4936—5030
Invariants of a correspondence      G.20
Invariants of a pair of homog. functions      Q.1
Invariants of a quadric      J.86
Invariants of a quadric, of two      M.24 Q.6
Invariants of a quintic, of 12th order      Q.1
Invariants of a quintic, of 18th order      C.92 J.59
Invariants of an orthogonal transformation      J.65 LM.13
Invariants of binary cubics      An.65
Invariants of binary forms, of 8th deg.      C.84 G.2 M.5
Invariants of binary forms, of 8th deg., simultaneous      M.1
Invariants of binary forms, of higher transformations      J.71
Invariants of binary forms, superior limit to number of irreducible      C.86
Invariants of d.e linear      C.88
Invariants of d.e linear, of 4th order      Ac.3
Invariants of linear transformations      M.20
Invariants of particular conics      4945
Invariants of points, lines, and surfaces      Q.4
Invariants of sixth order      G.19
Invariants of ternary forms      G.19
Invariants of three conics      Q.10
Invariants of two conics      4936 N.75
Invariants, differential      M.24
Invariants, differential, of given order and degree belonging to a binary 10-ic      C.89
Invariants, mutual relation of derived invariants      J.85
Invariants, partial      LM.2
Invariants, related to linear equations      C.94
Invariants, skew, of binary quintics, sextics, and nonics, relations      AJ.1
Invariants, transformation theorem      M.8 Me.85
Inverse calculus of differences      N.51
Inverse equation of a curve or inverse method of tangents      5160 No.1780 J.26 Mem.9 26
inversion      1000 5212 An.59 C.94 pr90 LM.5 Me.66 thsN.61 Pr.34
Inversion and stereographic projection      E.35
Inversion, formulae      An.53
Inversion, formulae, Lagrange's      J.42 54
Inversion, of 2 non-intersecting circles into concentric circles      E.39
Inversion, of a curve      5212 G.4 J.14 Pr.14
Inversion, of a curve, angle between radius and tangent      5212 5219 E.30
Inversion, of a plane curve      5212 G.4 Pr.14
Inversion, of a quadric      J.52 76 Q.11
Inversion, of a system of functions      An.71
Inversion, of arithmetical identities      G.23
Inversion, problems by Jacobi      J.89 geo. Q.7
Involute      5149 5153 5166
Involute and evolute in space      CD.6
Involute of a circle      5306 C.26
Involute of a circle, successive      E.34
Involute of a tortuous curve      5753
Involute, integrals of oblique      C.85
Involution      1066 A.55 63 gzAn.59 At.63 CD.2 thCP.11 thE.33 G.10 20 J.63 N.53 64 65
Involution and application to conics      A.4 5
Involution of 6 lines in space      C.52
Involution of a circle      Me.66
Involution of a cubic space and the resulting complex      Z.24
Involution of higher degrees      N.99 JM.72
Involution of higher degrees, of 3rd and 4th      An.84 Z.19
Involution of n-tic curves      C.87
Involution of numbers, machine for      P.15
Involution of points on a conic      N.82
Involution of right lines considered as axes of rotation      C.52
Involution relation between a curve and an n-tic, the latter having a multiple point of the n-1th order      C.96
Involution, pencils with problems in conics and cubics      N.85
Involution, systems of points in      4826 4828
Involution, systems of points in, ditto, marked on a surface      C.99
Irrational fractions, decomposition of      J.19
Irrational fractions, irreducibility of      Mem.41
Irrational fractions, rationalization of      A.18
Irrational functions      M.4
Irrational functions of the 2nd degree      C.98
Irreducible functions with respect to a prime modulus      C.70 90 93 L.73
Isobaric, algorithm      N.84
Isobaric, calculus      N.85
Isobaric, homog. functions      G.22
Isogonal relations      A.60 Z.18 20
Isogonal relations, do. represented by a fractional function of the 2nd degree      M.18
Isogonal relations, representation of $x=\sqrt[n]{X}$ and $x^{m} \sqrt{ \frac{aX^{n}+b}{cX^{n}+d}}$      Z.26
Isogonal relations, transformation of plane figures      N.69
Isomerism, pr      AJ.1
Isoperimeters, method of      N.47 74 82
Isoperimeters, problems      J.18 M.13 Mel.5
Isoperimeters, triangle with one side constant, and a vertex at a fixed point      C.84
Isoptic loci      Pr.37
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