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

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1970

Количество страниц: 988

Добавлена в каталог: 07.05.2008

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Предметный указатель

Series, $1^{p} - 2^{p} + 3^{p} - ...$ & $1^{p} - 3^{p} + 5^{p} - ...$       J.7
Series, $a \pm nb + C (n, 2)c \pm \& c.$       J.31
Series, $n^{r} - n (n - 1)^{r} + C (n, 2) (n - 2)^{r} - ...$       285
Series, $n^{r} - n (n - 1)^{r} + C (n, 2) (n - 2)^{r} - ...$ , r = n      CM.1
Series, $x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + ... = e^{x} - 1$       150
Series, $x + \frac{x^{2}}{2} + \frac{x^{3}}{3} + ... = \log \frac{1}{1 - x}$       156
Series, $x + \frac{x^{3}}{3} + \frac{x^{5}}{5} + ... = \frac{1}{2} \log \frac{1 + x}{1 - x}$       157
Series, $x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - ... = \log (1 + x)$       155
Series, $x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - ... = \sin x$       764
Series, $x - \frac{x^{3}}{3} + \frac{x^{5}}{5} - ... = \tan^{-1} x$       791
Series, $x - \frac{x^{7}}{7!} + \frac{x^{13}}{13!} - ...$       E.44
Series, $x - \frac{x^{7}}{7!} + \frac{x^{13}}{13!} - ...$ with x = 1      J.5
Series, $\frac{x^{2}}{2!} - \frac{x^{4}}{4!} + \frac{x^{6}}{6!} - ... = 1 - \cos x$       765
Series, $\sum (-1)^{n} \frac{x^{n}}{(a + 2n) (1 - x)^{n}}$       Q.6
Series, $\sum (-1)^{n} \frac{x_{-1}^{(n)}}{n + 1!}$       A.26
Series, $\sum (a + n)^{b} x^{n}$       N.56
Series, $\sum (a_{n} + b_{n} x^{c})x^{k - n}$       Z.15
Series, $\sum a_{n} x^{(n)}$       2709
Series, $\sum A_{n} \cos^{n} \theta {\cos \atop \sin} n \theta$       Z.1
Series, $\sum A_{n} \phi (n)x^{n}$       J.25 28
Series, $\sum c^{n} {\sin \atop \cos} (\alpha + n \beta)$       783
Series, $\sum f (n) {\sin \atop \cos} n \theta$       J.42 L.52
Series, $\sum f (nx)$       L.51
Series, $\sum H (m , n)x^ {n} {\sin \atop \cos} n \phi$       J.41
Series, $\sum K_{n} \frac{x^{n_{\alpha} + \beta}}{n \alpha + \beta}$ , $\beta$ a pos. integer < $\alpha$ , $K_{n}$ = the general term of some recurring series      C.86
Series, $\sum n^{a} x^{n}$       A.27
Series, $\sum \frac{(n - 1)x^{n}}{n!a^{n - 1}}$       A.50
Series, $\sum \frac{1.3...2n - 1}{n! 2^{n} (2n + 1)}$       L.60
Series, $\sum \frac{1}{(a + nd)^k}$       N.59
Series, $\sum \frac{1}{2^{n}} \tan \frac{\phi}{2^{n}}$       A.44
Series, $\sum \frac{1}{x^{(n)}}$       E.56
Series, $\sum \frac{a}{n^{1 + a}}$       A.34
Series, $\sum \frac{c^{n}}{n!} {\sin \atop \cos} (\alpha + n \beta)$       788
Series, $\sum \frac{n \sin n\theta}{a^{2} + n^{2}}$       2962 M.5
Series, $\sum \frac{n^{x}}{a^{n}}$       A.41
Series, $\sum \frac{n^{x}}{n!}$       A.61
Series, $\sum \frac{x^{n}}{n^{2}}$       Mem.11
Series, $\sum \frac{x^{n}}{n^{2}}$ with x = 1      J.5
Series, $\sum \frac{x}{an^{m} + a_{1} n^{m - 1} + ... + a_{m}}$       A.35
Series, $\sum \left( a^{n} {sin \atop \cos} n \phi \left) / n$       2922—2923
Series, $\sum \left( {\sin \atop \cos} 2n + 1 \phi \right) / n^{k}$       J.54
Series, $\sum \left( {\sin \atop \cos} 2n + 1 \phi \right) / n^{k}$ with k = 2      2960—2961 J.8
Series, $\sum \left( {\sin \atop \cos} n \phi \right)^{2\ or\ 4} / n^{4}$ and $\sum \left( {\sin \atop \cos} n \phi \right)^{3} / n^{3}$       L.73
Series, $\sum \left\{ \left( \frac{n + 1}{1} \right) \left( \frac{s - 3}{0} \right) + ... \right\}$       G.11
Series, $\sum \sin^{3} (2n + 1) \phi / (2n + 1)^{4}$       E.39
Series, $\sum {\sin \atop \cos} (\alpha + n \beta)$       800 Q.3
Series, $\sum {\sin \atop \cos} n^{2} \frac{2r\pi}{p}$       L.40
Series, $\sum_{1}^{m} f (x + \frac{n}{m})$       A.22
Series, $\sum_{n = 1}^{n = \frac{q - 1}{2}} E \left( n \frac{p}{q} \right)$       C.50
Series, a paradox      Me.72
Series, a.p and g.p combined      A.9
Series, application      thA.48
Series, application to arith      G.7
Series, binomial      see "Binomial theorem"
Series, binomial, analogous series      E.35 J.32 N.82
Series, binomial, analogous series with inverse binomial coefficients      Me.80
Series, coefficients independently determined      A.18
Series, combination      A.26
Series, convergent and of d.i with a periodic factor      L.53
Series, convergent and products, condition      M.22
Series, convergent in Kepler's problems      Ac.1799
Series, convergent whose terms are continuous functions of the same variable      C.36
Series, convergent, multiplication of      M.24
Series, convergent, power-series      A.25
Series, convergent, representing functions      M.5 22
Series, convergent, representing integrals of d.e      C.40
Series, convergent:      239 A.2 6 8 14 26 41 67 69 No.44 C.10 11 28 40 43 J.2 3 11 13 16 22 42 45 76 L.39—42 M.10 20—22 Me.64 N.45 46 67 69 70 P.87 Z.10 11
Series, converted into continued fractions      J.32 33 Mem.9
Series, converted into products of an infinite no. of factors      J.12 L.57 N.47
Series, deduction from $\left( \sum \frac{a_{2}^{(n)} x^{n}}{a^{(n)} n!} \right)e^{-x} = \sum \frac{x^{2n}}{(a + 1)_{2}^{(n)} 2^{n} n!}$       LM.9
Series, derived      A.22
Series, derived from $\tan^{-1} \theta$       A.16
Series, developed in elliptic integrals of 1st and 2nd kind      An.69
Series, difference      264 A.23 24
Series, differential transf. and reversal of      Pr.7
Series, Dirichlet's f. for $\sum \left( \frac{n}{p} \right) \frac{1}{n}$       C.21 L.46
Series, discontinuous      CP.6 L.54 Me.78 82 N.85
Series, divergent      A.64 No.68 C.17 20 CP.8 10 J.11 13 41 M.10 Z.10
Series, division of      AJ.5
Series, double      C.63
Series, doubly infinite      CD.6 M.24
Series, ext. of by any parameter      A.48
Series, factorial      268 Mem.20 N.67 TE.20
Series, Fourier's      A.39 C.91 92 96 CM.2 Z.27
Series, Gregory's      791
Series, harmonic periodic      J.23 25
Series, integration of infinite      A.3
Series, involving two angles      L.74
Series, irrationality of some      J.37
Series, Klein's higher      An.71
Series, Laplace's (d.c)      C.68
Series, limits of      A.20 Me.76
Series, limits of, by the method of means      J.13
Series, limits of, remainders      C.34
Series, modular      C.19
Series, multiple      C.19
Series, multiple, "regulateur" of      C.44
Series, neutral      CP.11
Series, obtained by inversion from Taylor's series      Mem.11
Series, periodic, critical values of      CP.8
Series, products of contiguous terms of      Mem.18
Series, recurring      251
Series, recurring, doubly      An.57 J.33 38 Me.66 Mem.24 26 N.84
Series, recurring, of circles and spheres      N.62
Series, recurring, of circles and spheres, f      Z.14
Series, represented by rational fractional functions      J.30
Series, reversion of      551 J.52 54 LM.2 TI.7
Series, self-repeating      CP.9
Series, transformation of      C.59 J.7 9
Series, transformation of $\sum \int f (x, t) dt$ and others      C.13
Series, transformation of, into a continued fraction      Mem.20 Z.7
Series, trigonometrical      A.63 Ac.2 C.95 97 M.4—6 16 17 22 24 J.71 72
Series, trigonometrical, conversion in multiples of arc      L.51
Series, trigonometrical, representing an arbitrary function between given limits      J.4
Series, trigonometrical, symbolic transf. of      Q.3
Series, triple      G.9
Series, two infinite, multiplication rule      J.79
Seven planes problem      N.56
Seven-point circle      4754c
Sextactic points of plane curves      Pr.13 14
Sextic curves and ellipse, pr      J.33
Sextic curves, $ax^{\frac{2}{3}} + by^{\frac{2}{3}} + c^{\frac{2}{3}} = 0$       Q.15
Sextic curves, bicursal      LM.7
Sextic curves, mech.cn      LM.2
Sextic developable      Q.7 9
Sextic equation      C.64 M.20
Sextic equation, irreducible      J.37
Sextic equation, solution when the roots are connected by $(\alpha - \beta) (b - \gamma) (c - a) + (a - b) (\beta - c) (\gamma - \alpha) = 0$       J.41
Sextic torse      An.69
Sextinvariant to a quartic and quart-invariant to a sextic      AJ.1
Shortest distance between two lines      5534 A.46 G.5 N.49 66
Shortest distance between two points on a sphere      A.14 N.14 67 68
Shortest distance from the centre of a surface      A.63
Shortest distance of a point from a line or plane      N.44
Shortest line on a surface      A.23 37 64
Shortest line on a surface in spheroidal trigonometry      A.40
Signs      CP.2 11 J.12 Me.73
Signs, $(\pm)$       CD.6 7 Me.85 N.48 49
Signs, (=)      Me.75
Similarity of curves and solids      A.13
Similarly varying figures      LM.16
Simpson's f. in areas      2992 C.78
Simson line of a triangle      E.29
Sine and cosine in factors      807 A.27 J.27 L.54
Sine and cosine of $(a \pm b)$       627 A.6 21 36
Sine and cosine of infinity      CP.8 Me.71 Q.11
Sine and cosine of multiple arcs      CM.4 TI.7 see
Sine and cosine of particular angles      690
Sine and cosine of particular angles, $3^{\circ}$ , $6^{\circ}$ ,...to $90^{\circ}$       N.53
Sine and cosine, extension of meaning      A.31 C.86

Sine and cosine, sums of powers      An.1
Sine and cosine, tables, formation of      688 A.66 N.42
Sine and cosine, values near 0 and $90^{\circ}$       G.9
Sines of higher orders      C.91 92
Sines of higher orders, ap. to d.e      C.90 91
Sines, natural, limit of error      N.43
Six points on a plane or sphere      LM.2
Six-point circle of a triangle      Me.82 83
Skew surfaces      see "Scrolls"
Sliding rule      LM.6
Small quantities of second order      1410
Smith's Prize questions, solutions      Me.71 72—74 77
Solid angle      A.42
Solid angle, section of      No.19
Solid harmonics      Me.80
Solid of revolution      A.60 67
Solid of revolution between two ellipsoids      A.2
Solid of revolution, cubature and quadrature of      5877—5880 A.68 N.42
Space homology      G.20
Space theories      An.70 LM.14 P.70 Z.17 18
Space theories, 21 coordinates of      LM.10
Space theories, 3-dim.      J.83
Space theories, 4-dim.      J.83 M.24
Space theories, 6-dim.      G.12
Space theories, absolutely real space      G.6
Space theories, angles (4-dimen.)      A.69
Space theories, areas and volumes      A.69 CD.7
Space theories, bibliography of      AJ.1 2
Space theories, circle      G.12 16 18
Space theories, conics      AJ.5
Space theories, continuous manifoldness of two dimensions      LM.8
Space theories, curves      C.79 M.18
Space theories, Feuerbach's points      G.16
Space theories, Grassmann's "Ausdehnungslehre"      AJ.1 CP.13 M.7 12 Z.24
Space theories, Grassmann's "Ausdehnungslehre", ap. to mechanics      M.12
Space theories, hyperboloid      Z.13
Space theories, imaginary quantities      Z.23
Space theories, loci (anal.)      C.24
Space theories, non Euclidean or n-dimensional      A.6 29 58 ths64 AJ.4 5 An.71 C.75 G.6 10 12 23 M.4 5—7 Me.ths68 72 Pr.37
Space theories, plane triangle      A.70
Space theories, planes (4-dimen.)      A.68
Space theories, Plucker's "New geometry of"      G.8 L.66 P.11 Z.11 12
Space theories, point groups      thsAc.7
Space theories, polars and alg. forms      J.84
Space theories, potential function      An.82 83
Space theories, projection      M.19
Space theories, projection, 4-dim. into 3-dim.      AJ.2
Space theories, quadric, super lines of (5-dim.)      Q.12
Space theories, quaternions      CP.13
Space theories, regular figures      AJ.3
Space theories, representation by correlative figures      C.81
Space theories, reversion of a closed surface      AJ.1
Space theories, screws, theory in elliptic space      LM.15 16
Space theories, simplicissimum of nth order      E.44
Space theories, space of constant curvature      An.69 73 J.86 M.12
Sphere, 16 touching 4 spheres      J.37 JP.10 Me.cn82 Mem.10 N.44 47 65 66 84 Z.14
Sphere, 4 spheres, pr.      L.46
Sphere, 4 touching a 5th      At.19
Sphere, 5 points of      J.23 N.84
Sphere, 8 touching 4 planes      E.19 N.50
Sphere, and circle, geo      A.57
Sphere, cn. from 4 conditions      JP.9
Sphere, cutting 4 spheres at given angles      An.51 N.83
Sphere, cutting a sphere orthogonally and touching a quadric, locus of centre      TI.26
Sphere, diameters, no. of all imaginable      A.24
Sphere, equation of      5582
Sphere, geo      C.92
Sphere, illumination of      Z.27
Sphere, kinematics on a      LM.12
Sphere, q.c      Me.62
Sphere, sector of (eccentric)      A.65
Sphere, small circle of      Me.85
Sphere, ths and prs      M.4
Sphere, touching an equal sphere      E.31 32
Sphere, touching an equal sphere, as many as possible      A.56
Sphere, volume, &c. of segment and zone      6050 A.3 32 39 An.57 P.1
Spherical areas      902
Spherical catenaries      J.33
Spherical class cubics with double foci and cyclic arcs      Q.15
Spherical conics      thQ.3
Spherical conics and quadrangle      Q.13
Spherical conics, homofocal      L.60
Spherical coordinates      CD.1 CM.1 ap2
Spherical coordinates, homogeneous      G.6
Spherical curvature      5728 5740 5747 thE.34
Spherical curves      A.35 36 Mem.10
Spherical curves and polars      No.63
Spherical curves of 3rd class with 3 single foci      Q.17
Spherical curves of 4th class with quadruple foci      Q.18
Spherical curves of 4th order      J.43
Spherical curves with elliptic function coordinates      J.93
Spherical curves, equidistant      An.71 J.25
Spherical curves, rectification of      An.54
Spherical ellipse      t.c Q.8
Spherical ellipse, quadrature, &c.      L.45 N.48 54
Spherical epicycloid      G.12
Spherical excess      Mel.2
Spherical excess of a quadrilateral      Me.75
Spherical excess, cn      N.46
Spherical excess, f      Z.6
Spherical figures, division of      J.22
Spherical geometry      G.4 J.6 8 13 thsl5 22 M.15 N.48 58 59 Q.4 TI.8
Spherical harmonics or "Laplace's functions"      An.68 C.86 99 CD.1 CM.2 J.26 56 60 geo 70 80 82 90 L.45 48 LM.9 Me.77 78 85 P.57 Pr.8 18 Q.7 Z.24
Spherical harmonics or "Laplace's functions" and connected d.i      Q.19
Spherical harmonics or "Laplace's functions" and homogeneous functions      CM.2
Spherical harmonics or "Laplace's functions" and potential of ellipse and ellipsoid      P.79
Spherical harmonics or "Laplace's functions" and ultra-spherical functions      Z.12
Spherical harmonics or "Laplace's functions" as determinants      Me.77
Spherical harmonics or "Laplace's functions", $b_{s}^{(i)}$ by continued fractions      JP.28
Spherical harmonics or "Laplace's functions", $b_{s}^{(i)}$ by continued fractions, $\int_{0}^{1} Q_{n} Q_{n^{'}}$       P.70
Spherical harmonics or "Laplace's functions", $P^{n} (\cos \gamma)$ , $n = \infty$       J.90
Spherical harmonics or "Laplace's functions", $P^{n} (\cos \gamma)$ , $n = \infty$ , $\int_{-1}^{1} P_{i} \mu^{m} d \mu$ , &c.      Q.17
Spherical harmonics or "Laplace's functions", analogues of      J.66 LM.11
Spherical loci in spherical coordinates      TE.12
Spherical oblong      An.52
Spherical oblong, area      J.42
Spherical polygonometry      J.2
Spherical polygons in- and circum-scribed to small circles of the sphere, by elliptic transcendents      J.5
Spherical quadrilateral      A.4 40
Spherical quadrilateral, surface of      A.34 35
Spherical quadrilateral, th      E.28 N.45
Spherical quartics, foci      Q.21
Spherical quartics, foci, 4-cyclic and 3-focal      LM.12
Spherical representation of surfaces      C.68 75 94 96 M.13
Spherical surface represented on a plane      Me.73
Spherical triangle      A.9 ll 20 ths50 65 E.f30 J.10 pr28 JP.2
Spherical triangle and circle      898 A.29 33
Spherical triangle and differentials of sides and angles      A.10
Spherical triangle and ex-circles      898 E.30
Spherical triangle and plane triangle      A.1
Spherical triangle and plane triangle of the chords      A.33 An.54 Z.1
Spherical triangle by small circles, area      N.53
Spherical triangle of very small sides      N.62
Spherical triangle, ambiguous case      Me.77 85
Spherical triangle, angles of, calculated from sides      A.51
Spherical triangle, cos (A + B + C), f.      Me.72
Spherical triangle, graphic solution      AJ.6
Spherical triangle, right angled      881 A.51
Spherical triangle, right angled, solution by a pentagon      A.11
Spherical triangle, two, relations of sides and angles      A.2
Spherical trigonometry      876 A.ths2 11 13 28 37 J.prs6 13 LM.11 N.42 Z.16
Spherical trigonometry, Cagnoli's th.      904
Spherical trigonometry, cot a sin b      Me.64
Spherical trigonometry, cot a sin b, mnemonic      895 CM.3
Spherical trigonometry, d.e of circles      Q.20
Spherical trigonometry, derived from plane      A.26 27
Spherical trigonometry, formulae      882 A.5 16 24 26 N.45 46 53
Spherical trigonometry, formulae, ap. in elliptic functions      A.40
Spherical trigonometry, formulae, graphically      A.25
Spherical trigonometry, Gauss's eqs.      897 A.13 17 J.7 12 LM.3 13

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