Carr G.S. — Formulas and Theorems in Pure Mathematics :: Электронная библиотека попечительского совета мехмата МГУ

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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:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Издание: Second Edition

Год издания: 1970

Количество страниц: 988

Добавлена в каталог: 07.05.2008

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Expansion of $\frac{x}{e^{x}\pm 1}$ , $\frac{e^{x}-1}{e^{x}+1}$       1539 1543—1544
Expansion of $\int^{n}_{0}u_{x}dx$ in terms of $u_{0}, u_{1}, u_{2}, &c.$       3778
Expansion of $\int^{\infty}_{0}e^{-ax}{sin \atop cos}bxdx$ and summation of the series      J.41
Expansion of $\phi(a+bx+cx^{2}+...)$ (Arbogast)      1536 CD.1 6
Expansion of $\phi(e^{t})$ (Herschel)      3757
Expansion of $\pi$       2931—2932 2945 2960—2962 Me.78
Expansion of $\pi$ , powers of $\pi$       Me.78
Expansion of $\pi$ , powers of $\pi^{-1}$       Me.83
Expansion of $\pi$ , powers of $\pi^{2}$       858
Expansion of $\theta$ $cot\theta$ in powers of $sin^{2}\theta$       Q.6
Expansion of $\{(1-\frac{t}{2^{n}})(1-\frac{t}{3^{n}})...\}^{-1}$       J.40
Expansion of $\{(x-a_{1})^{2}+...+(x-a_{4})^{2}\}^{-1}$       C.95
Expansion of ${sin \atop cos}(\theta+\theta_{1}+...+\theta{n-1})$       A.34
Expansion of ${sin \atop cos}nx/cos x^{n}$       A.4
Expansion of a function of $y, y^{'}$ in ascending powers of $x, x^{'}$ when $y= z+x\phi(y)$ and $y^{'}=z^{'}+x^{'}\phi(y^{'})$ as in 1552      J.48
Expansion of a function of a complex variable      M.19
Expansion of a function of a function      AJ.2 3
Expansion of a function of a rational fraction      At.65
Expansion of a function of n variables      C.60 J.66
Expansion of a polynomial      137 Z.26
Expansion of a quartic function      A.35
Expansion of alg. functions      C.89 Z.45
Expansion of alg. functions, Eisenstein's th      J.45
Expansion of an arc in linear functions of sines or tangents of fractions of the arc in g.p      L.43
Expansion of Bernoulli's numbers      1545
Expansion of circular functions      J.24 Q.5
Expansion of cosec x      2914 2918
Expansion of cot x      2911 2916 C.88 Q.17
Expansion of differential coefficients by f.d.c and the converse      J.16
Expansion of do. when $x = \frac{log y}{y}$       1570
Expansion of elliptic functions      A.19
Expansion of elliptic functions and of their powers      C.83
Expansion of elliptic functions and of their powers, cos amx      L.64
Expansion of equations      L.50
Expansion of exponential functions      N.82
Expansion of f(0) (Bernoulli)      1510
Expansion of f(x) (Maclaurin)      1507 3759
Expansion of f(x+h)      1500—1509 1520 see
Expansion of f(x+h), Abel's th      1572
Expansion of f(x+h), Boole      1547 AJ.3
Expansion of f(x+h), Stirling      1546
Expansion of f(x+h, y+k)      1512 1521
Expansion of f(x, y)      1516 1523 Me.3
Expansion of f(y) in powers of $\psi(y)$ (Burmann)      1559
Expansion of fractions      248
Expansion of functions of infinitesimals      G.12
Expansion of functions, $Al(x), Al_{1}(x), Al_{2}(x)$ (Weierstrass's functions) in powers of the modulus      C.82 85 86 L.79
Expansion of higher integrals of log x      A.4
Expansion of holomorphic functions      M.21
Expansion of holomorphic functions by arcs of circles      C.94
Expansion of implicit functions      551 1550 L.81
Expansion of integrals      A.1
Expansion of integrals of linear d.e      An.71
Expansion of integrals of log x      A.4
Expansion of log y and $log y^{n}$ in powers of $a^{-1}$ when $y^{3}-ay+b=0$       1553—1554
Expansion of logarithms      152—159 N.82
Expansion of n, alg. functions from n eqs      G.11
Expansion of nth derivative of $\surd(a^{2}-b^{2}x^{2})$       A.4
Expansion of numbers      M.21
Expansion of powers of arc in powers of sines      J.11
Expansion of sec x      1526 A.16 C.88 J.26
Expansion of sin $\theta$ and cos $\theta$ in powers of $\theta$       764 1531 A.5 29 C.16
Expansion of tan x      1525 2913 2917 A.16 C.88 N.57
Expansion of xexp.[xexp.[xexp, &c.      J.28
Expansion of y in powers of x when $x=\frac{sin y}{sin(y+a)}$       796 1558
Expansions of a function in a series      A.31 An.7 thsAJ.3 4 C.7 13 17 20 CM.4 J.90 L.38 46 76 M.16 Mel.3 Mem.33 N.82 83 see "Summation"
Expansions of a function in a series by a series      C.93 95
Expansions of a function in a series by Bessel's function      J.67 M.10 17 Z.1
Expansions of a function in a series by binomial theorem      125
Expansions of a function in a series by factorials      3730
Expansions of a function in a series by generating functions      3732
Expansions of a function in a series by indeterminate coefficients      232 1527—1534 A.3
Expansions of a function in a series by logarithmic method      C.9
Expansions of a function in a series by Maclaurin's th      1524
Expansions of a function in a series of another function      1559 C.95 96
Expansions of a function in a series of circular functions      2955 A.11 CM.3 J.43 L.36 Q.12
Expansions of a function in a series of circular functions of imag. arcs      J.6
Expansions of a function in a series of denominators of convergents      C.46 JP.21
Expansions of a function in a series of explicit functions      1500—1547
Expansions of a function in a series of exponentials      J.80
Expansions of a function in a series of faculties of the variables      Mem.31
Expansions of a function in a series of implicit functions      1550—1573
Expansions of a function in a series of Jacobian functions      An.82
Expansions of a function in a series of Legendre's functions, $X_{n}$       An.75
Expansions of a function in a series of periodic quantities      C.52 53 JP.11
Expansions of a function in a series of powers of a polynomial      C.86 J.53 88
Expansions of a function in a series of powers of another function      Mem.33 N.74
Expansions of a function in a series of powers of the variable      At.57 C.19 L.46
Expansions of a function in a series with limits      C.34
Expansions of a function in a series within a given interval according to the mean values of the function and of its successive derivatives in this interval      C.90
Expansions of a function in a series, coefficients of, gn form      C.85
Expansions of a function in a series, coefficients of, gn form, gn property      J.41
Expansions of a function in a series, connected with a 2nd order d.e      C.5 L.36 37
Expansions of a function in a series, extended class of      C.82
Expansions of a function in a series, extended class of, approximating to functions of very large numbers      L.78
Expansions of a function in a series, num      Q.3 Z.2
Exponentia1, th, functions      P.16
Exponentia1, th, replaced by an infinite product      C.99
Exponential, th      149 N.52
Exponentials, successive of Euler      L.45
Exponents      N.57 P.1776
Exponents, reduction for d.i      C.16
Factorials, $1, 2^{2}, 3^{3}...n^{n}$       Me.78
Factorials, $n!=n^{n}e^{-n}\surd(2n-pi)$ (Stirling)      Q.15
Factorials, $n!=\Gamma(1+n)$       2290
Factorials, $n!=\Gamma(1+n)$ , approx. to when n is large      C.9 50 J.25 27 L.39
Factorials, $\frac{1.3.5...}{2.4.6...}$ theorem      339
Factorials, $\{2^{2p+1}p!m^{(p+1)}\}$       CM.3
Factorials, C(n, r) when $n=a+i\beta$       J.43
Factorials, calculus of      L.57 N.60 Pr.22 Q.12 Q.f8
Factorials, geom. i.e $(1+x)(1+rx)(1+rx^{2})...$       C.17
Factorials, notation      94 2451 Q.2
Factorials, reciprocal      C.17
Factorials, treatment by limits      J.39
Factors      1—27
Factors in analysis of integral functions      M.15
Factors of $(x+y)_{n}-x^{n}-y^{n}$       thQ.15 16
Factors of $Ax^{2}+By^{2}+Cz^{2}$ , th of Lagrange      AJ.3
Factors of $x^{2n}-2x^{n}y^{n}cos n\theta+y^{2n}$       807
Factors of $x^{2}-fgy^{2}=\pm 1$       A.33
Factors of $x^{n}-2ncosn\theta+x^{-n}$       CP.11 Me.76
Factors of an equation      400 J.3
Factors of an equation, condition for a factor of the form $x^{n}-a^{n}$       A.55 63
Factors of composite numbers      274 J.11
Factors of polynomials and geo.ap      J.29 89
Factors, $(1-x)(1-x^{2})(1-x^{3})...$       C.96
Factors, application to rotations to indicate direction      J.28
Factors, complex      C.24
Factors, equal, of integral polynomials      C.42 L.56
Factors, irreducible, of an integral function according to a prime modulus p      C.86
Factors, linear, resolution into      N.82
Factors, of 100...01      Me.79
Factors, product of an infinite number of      A.59
Factors, product of an infinite number of, $cos\frac{x}{2}cos\frac{x}{4}cos\frac{x}{8}...$       N.70
Factors, radical, of numbers      C.24 25
Factors, tables of (Burchardt's) p.7      to 4100 J.46
Factors, tables of (Burchardt's) p.7, geo. properties      J.22
Factors, transformation of      A.57
Faculties, analytical      J.7 11 33 35 40 44 51
Faculties, analytical, coefficients of      A.9 11 At.75
Faculties, analytical, divisibility of      A.48
Faculties, analytical, numerical, of 2nd order      Mem.38
Faculties, analytical, series      Z.4
Fagnani's theorem      6088 A.26 LM.5 13 23 Z.1
Fagnani's theorem, curves having Fagnanian arcs      LM.11
Fagnani's theorem, stereometric analogy      Z.17
Faisceaux of binary forms having the same Jacobian      C.93
Faisceaux of circles      C.76
Faisceaux of conics      Z.20
Faisceaux of lines and surfaces      N.53 83

Faisceaux of tortuous cubics in connection with ray-complexes      Z.19
Faisceaux, curvature relations      Z.15
Faisceaux, formation of      C.45 CM.3
Faisceaux, intersections of      N.72
Faisceaux, intersections of, degree of the resulting curve      J.71
Faisceaux, plane      N.53
Faisceaux, plane, defined by a first order d.e      C.86
Fan of Sylvester      E.33
Faure's theorems      Gr.1 19
Faure's theorems and Painvin's      N.61
Fermat's theorems of $(N^{p-1}-1)\div p$       369 A.32 AJ.3 J.8
Fermat's theorems of $x^{n}+y^{n}=z^{n}$ being insoluble when n is an odd prime, &c      An.57 C.gz84 96 91 J.40 87 TE.21
Fermat's theorems of $x^{n}+y^{n}=z^{n}$ , $x+y=\cap$ , $x^{2}+y^{2}=\cap^{2}$       Mem.26
Fermat's theorems of $x^{n}+y^{n}=z^{n}$ , analogous theorem      J.3
Fermat's theorems of $x^{n}+y^{n}=z^{n}$ , and periodic functions      Me.76
Fermat's theorems of $x^{n}+y^{n}=z^{n}$ , case of n=14      J.9
Fermat's theorems of the semicircle      A.27 30 31 gzA.31
Fermat's theorems of the semicircle, method of maxima      C.50
Feuerbach's, th of the circle      A.59
Feuerbach's, th of the triangle      Me.84
Fifteen girl problem      E.34 35 Q.8 9
Figurate numbers      289 A.5 69
Finite difference equations      AJ.4 An.59 CD.2 CM.1 3 4 CP.6 JP.6 L.83 P.60 Pr.10
Finite difference equations of integrable form      C.54
Finite difference equations of mixed differences      Q.10
Finite difference equations of the kind $u_{x, y}=u_{x-y, x+y}$       CM.4
Finite difference equations, linear      AJ.7 An.50 At.65 Q.1
Finite difference equations, linear, determination of arbitrary constants      A.27 At.65 G.7
Finite difference equations, linear, first order, constant coefficients      C.8
Finite difference equations, linear, integration to differences of any order      J.12
Finite difference equations, linear, with variable coefficients      C.17
Finite difference equations, partial, constant coefficients      C.8
Finite difference equations, partial, linear of 2nd order      C.98
Finite difference equations, partial, of physics      C.73
Finite differences of functions of zero      TI.17
Finite differences of powers converted into d.i      JP.17
Finite differences, calculus of      3701—3830 A.13 18 24 63 C.70 J.11 12 13 14 15 16 Me.82 Mel.5 Mem.13 N.69 thsP.16 17
Finite differences, calculus of $hu^{'}_{x}=\delta u_{x}-\frac{h}{2}\delta u^{'}_{x}+\frac{B_{1}h^{2}}{2}\delta u^{''}_{x}-&c.$       Ac.5
Finite differences, calculus of $\beta u_{0}, \beta^{2}u_{0}, &c.$ , in a function of $\Delta u_{0}, \Delta^{2}u_{0}, &c.$       N.61
Finite differences, calculus of $\Delta 1^{p}$ and Bernoulli's numbers      An.59
Finite differences, calculus of $\delta sinx$ and $\delta cos x$       CM.1
Finite differences, calculus of $\Delta^{2}u=0$       An.73
Finite differences, calculus of $\Delta^{n}0^{m}$       3744 Q.5 8 9
Finite differences, calculus of $\Delta^{n}0^{m}$ , Herschel's table      N.54
Finite differences, calculus of $\Delta^{n}0^{m}\div\Pi(m)$ table of      CP.13
Finite differences, calculus of $\Delta^{n}u$ in successive derivatives of u      3761 N.73
Finite differences, calculus of first and nth differences      3706
Finite differences, calculus of, ap. to complex variability      An.82
Finite differences, calculus of, ap. to complex variability, ap. to i.eq      An.50
Finite differences, exercises      No.44 47
Finite differences, formulae      CD.9 Q.2
Finite differences, formulae, sum and difference      J.58
Finite differences, H(n, r) value of      Q.9
Finite differences, integrals      C.39 57 JP.4 L.44
Finite differences, integrals, $\sum e^{x}y$       A.6 No.44
Finite differences, integrals, expressed by definite integrals      An.53
Finite differences, inverse method      C.74 P.7
Finite differences, involving $\sqrt[7]1$       Me.78
Fleflecnodal planes of a surface      Q.15
Flexure      AJ.2 Me.2
Flexure of ruled surfaces      An.65
Flexure of spaces      LM.9
Flexure of spherical surfaces      Me.77
Fluctuating functions      2955a LM.5 M.20 TI.19
Fluents      P.1786
Fluents of irrational functions      P.16
Focal properties of a parabola      1220 1223—1226 1230—1224 4231 4235—4238 G.22
Focal properties of a quadric surface      An.59 N.58
Focal properties of conics      1163 1167—1169 1181 1286—1288 4298—4306 4336—4345 4378 4382 4516 4550—4558 4719—4721 5008—5016 CD.7
Focal properties of curves      CD.7
Focal properties of homographic figures      N.71
Focal quadrics of a cyclide      Me.85
Focal, chords of conics      1226 4235 4339
Focal, circle of conics      Mel.2
Focal, distances      4298 N.64
Focal, pedal of a conic      N.66
foci      J.64 N.42 44 53 85 Q.2 a.c
Foci of cones      N.79
Foci of conics      1160 trA.25 63 64 cn69 gzC.22 L.39 CP.3 N.69 74 78 81 82 t.cQ.8 13 12 45
Foci of conics of four tangents      5029 N.83
Foci of conics through four points      N.83
Foci of conics, analogous points in higher plane curves      J.10
Foci of conics, coordinates of      4516
Foci of conics, eq. of      LM.11 o.cE.40
Foci of conics, exterior      N.79
Foci of conics, gen.eq      N.48
Foci of conics, locus, a cubic      M.5
Foci of conics, negative      A.64
Foci of conics, to find them      Q.25
Foci of conics, to find them, from gn.eq      5008
Foci of conics, under three conditions      Q.8
Foci of curves      C.82
Foci of curves, nth class      86 N.59 79
Foci of differential curve of a parabola      A.58
Foci of in conic of an n-tic, locus of      E.21
Foci of lines of curvature of an ellipsoid      Z.26
Foci of quadrics      N.42 66 74 75 78
Foci of quartics      J.56
Foci of surfaces      C.74
Foci of surfaces of revolution      N.74
Foci of the section of a quadric by a plane      N.64 70
Foci of the section of a quadric by another quadric      N.47
Folium of Descartes      5360 N.44
Forms, theory of      M.18
Forms, theory of higher degree      Mo.83 Pr.38
Forms, theory of reciprocity principle      An.56
Formula      G.15 19
Formulae for log 2, &c.      Me.79
Formulae in the Fund.Nova      Me.76
Formulae of reduction in i.c      1965 Me.3
Four colors problem      AJ.2
Four right lines not 2 and 2 in same plane      J.5
Four-point problem      E.5 6 8
Fourier — Bessel function      J.69 M.3
Fourier's formula in i.c      2726—2742 CM.3 J.36 69 L.36 M.4 Me.73 Q.8 gzZ.9
Fourier's formula in i.c, ap.to calculation of differentials      J.13
Fourier's theorem      518 528 An.50 75 J.13 M.19 Me.77 82 83
Fourier's theorem, ap. to a function of a complex variable      M.21
Fractions      AJ.3 G.9 pr16 J.88 L.10
Fractions, continued, decimal, partial, vanishing, &c.      AJ.3 G.9 pr16 J.88 L.10
Fractions, number expressible by $digits\leqq n$       C.96
Fractions, reduction to decimals      A.1 25
Fractions, transformation into decimals      A.11
Frullani's formula      2700 LM.9
Fuchs's theorem on $F(z, y, y_{z})=0$       C.99
Fuchsian functions      C.92 93 94 95 96
Functional equations      CM.3 J.90 TE.14
Functional equations, $f(x)=f(sin\frac{\pi x}{2})$       C.88
Functional equations, $f.\phi x=1+fx$       C.99
Functional equations, $f.\phi x=fx$       C.88
Functional equations, $f_{1}y.\phi x+f_{2}y.\phi_{2}x+&c.=f_{1}x.\phi_{1}y+f_{2}y+&c.$       J.5
Functional equations, $\int^{b}_{a}f(x, \theta)\phi(x+\theta)d\theta=F(x)$ , to find $\phi$       Pr.8
Functional equations, $\phi x+\phi y=\phi(xfy+yfx)$       J.2
Functional equations, $\phi x+\phi y=\psi\frac{fy.Fx+fx.Fy}{\chi(xy)}$       J.46
Functional equations, $\phi x-\phi\frac{ax+b}{cx+d}$       Q.15
Functional equations, $\phi.fx=F.\phi x$ , to find $\phi$       Mem.31
Functional images in ellipses      Q.17
Functional images in ellipses in Cartesian ovals      Q.18
Functional powers      Mem.38
Functional powers, symbols      Q.4
Functions from functional equations      M.24
Functions from Gauss's equation      C.92
Functions of 4 and 5 letters      L.56
Functions of 4, 5, and 6 letters      L.50
Functions of 6 variables which take only 6 different values through their permutation, not including 5 symmetrical permutations      A.68
Functions of 7 letters      C.57 95
Functions of a circular area from a given integral condition      Z.26
Functions of a real variable, connexion with their derivation      M.23 24
Functions of a variable analogous to the polynomials of Legendre      C.95
Functions of an analytical point, ths      C.95

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