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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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Предметный указатель

Functions of imaginary variables      C.32 48 JP.21 L.58 59 60 61 62 LM.geo
Functions of large numbers, approx.      C.20
Functions of n variables      C.21 Mo.83
Functions of n variables, with 2 n systems of periods      C.97
Functions of n variables, with 2 n systems of periods, analogous to sine and cosine      Q.16
Functions of n variables, with 2 n systems of periods, number of values      J.85
Functions of n variables, with 2 n systems of periods, number of values, do by permutation of the variables      C.21
Functions of n variables, with 2 n systems of periods, obtained from the inversion of the integrals of linear d.e with rational coefficients      C.90 J.89
Functions of real arguments, classification according to their infinitesimal variation      J.79
Functions of the species zero and unity      C.95
Functions of three angles, th.re 1st derivatives      J.48
Functions of three variables satisfying the d.e, $\Delta F=0$       Ac.4
Functions of two systems of quantities, correlative and numerically equal      C.98
Functions of two variables      Ac.3 C.90 96
Functions of two variables, f(x, y) such that f{zf(x, y)} is symmetrical      J.1
Functions of two variables, made constant by the substitution of a discontinuous group      C.97
Functions of two variables, which arise from the inversion of the integrals of two functions      C.92
Functions of two variables, whose ratio has a fixed limit      G.5
Functions which are neither rational nor reducible to irrational algebraic expressions      C.18
Functions which are of use in elliptic functions and logarithms      No.58
Functions which have no derivative throughout a certain interval      An.77
Functions which relate to the roots of the equation of division of a circle or of $n^{p}-1=0$       J.17
Functions which take a given value in a given position      An.82
Functions which vanish with their variables      TI.62
Functions whose logarithms are the sums of Abel's integrals of the 1st and 3rd kind      C.92
Functions whose successive derivatives form an arith. prog.      An.71
Functions with lacuna      C.96
Functions with linear transformations inter se      M.19 20
Functions with non-interchangeable periods      M.20 21 25
Functions with recurring derivatives      LM.4 TE.24
Functions, $E_{n}\equiv\frac{E^{n}}{1_{2}^{(n)}\pi}\int_{0}^{\pi}sin^{2n}\omega cos(e cos\omega)d\omega$       An.70
Functions, $G\equiv=\int_{0}^{1}\frac{tan^{-1}x}{x}dx=1-\frac{1}{3^{2}}+\frac{1}{5^{2}}-&.c=915965, 594177...$       Mem.83
Functions, $P\left({\alpha\beta\gamma \atop \alpha^{'}\beta^{'}\gamma^{'}}x\right)$       Z.14
Functions, $P^{m}(cos\gamma), n=0$       G.22
Functions, $x^{x}$       An.63
Functions, $Y(p, \phi)\equiv\int_{0}^{\phi}\frac{E(p, \phi)d\phi}{\surd\{1-p^{2}sin^{2}\phi\}}$ , X, Y, &c., such that $SXYd\sigma=0$ and that any function can be expanded in the form $aX+\beta Y+&c.$       LM.10
Functions, $\Gamma(x)$       see "Gamma function"
Functions, $\int\sqrt[3]{\{1+ax^{3}\}}dx$       J.9
Functions, $\phi(x)=\frac{ax+b}{cx+d}$       LM.9
Functions, $\Pi(z)\equiv\int_{0}^{\infty}x^{x}e^{-x}dx$ , $\psi(z)\equiv d_{z}log\Pi(z)$       Q.1
Functions, $\psi(a)$ of Jacobi      J.93
Functions, $\psi(x)\equiv d_{x}log\Gamma(x)$       2743
Functions, $\sum\int e exp(-z^{x})F(z)dz=0$       C.93
Functions, $\{(x^{x})^{x}\}^{x}$ and so on, and the corresponding inverse function      J.42
Functions, algebraic, alternating, analytical, circular, circulating, conjugate, continuous, curvital, cyclotomic, derived, discontinuous, elliptic, even and odd, exponential, Fuchsian, gamma, generating, hyperbolic, implicit, infinite, imaginary, integral, irrational, irreducible, isotropic, iterative, monodrome, monogenous, monotypical, non-uniform, periodic, polyhedral, quantitative, rational, representative, transcendental, trigonometrical      A.28 AJ.6 An.79 C.43 91 CP.1 J.16 prs71 74 84 87 91 L.45 Me.7 Mo.80 81 P.15 16 17 62 Pr.11 prsZ.26
Functions, allied to Pfaffians      Q.16
Functions, analogous to algebraic functions      C.89
Functions, analogous to circular functions      C.84
Functions, analogous to Euler's      C.89 M.19
Functions, analogous to functional determinants      J.75
Functions, analogous to modular functions      Ac.2 C.93
Functions, analogous, sine and cosine      Q.16
Functions, arising from $\surd(4-2xz+z^{2})$       J.2
Functions, Bessel's, $I(x)\equiv\frac{1}{\pi}\int^{\pi}_{0}cos(x cos\theta)d\theta=1-\frac{x^{2}}{2^{2}}+\frac{x^{4}}{2^{2}.4^{2}}-\frac{x^{6}}{2^{2}.4^{2}.6^{2}}+$ , Cauchy's numbers; $N_{-kj, p}\equiv\frac{1}{2\pi}\int^{2\pi}_{0}e^{-kui}(e^{iu}+e^{-iu})^{j}\times(e^{iu}-e^{-iu})^{p}du$ , cosine integral; $Ciq\equiv\int^{q}_{\infty}\frac{cos x}{x}dx$       taP.70
Functions, condition of f(x, y) being a function of $\phi(x, y)$       A.21
Functions, connected by a linear eq.      C.17
Functions, defined by d.e      JP.21 28
Functions, development of      see "Expansion"
Functions, differing very little from zero      L.74
Functions, Dirichlet's function, $F(x)\equiv\sum\left(\frac{D}{n}\right)\frac{1}{n^{x}}$       Z.27
Functions, do. through permuting the variables      JP.10 18 L.50 60
Functions, E(x)      Mel.6
Functions, elliptic, $\int x^{s-\gamma p-1}\vartheta(x^{p})\{R(x^{p})\}^{\pm\frac{s}{rp}}dx$       J.23
Functions, errors of geometricians      J.16
Functions, Euler's; B(l, m)      2280
Functions, expon-integral, $Eiq\equiv\int_{-q}^{\infty}\frac{e^{-x}}{x}dx$       A.10 taP.70
Functions, expressed by other functions, remainder      C.98
Functions, f(u, z), u being an implicit function of an imaginary variable z      Pr.42
Functions, f(x), formula of analysis      J.53
Functions, f(x)=0, y=f'(x), th. re $\phi(y)$       E.36
Functions, fractional      J.8
Functions, fractional, the variable being the root of an equation      N.56
Functions, Jacobi's, $\left(\frac{b}{a}\right)\equiv(-1)exp\sum_{i-1}^{i=\frac{a-1}{2}}e\left(\frac{bi}{a}\right)$       C.59 60 L.47 50
Functions, Lagrange, tr      JP.5 7
Functions, Laplace's $Y^{(n)}$       M.14
Functions, linear      C.90
Functions, log-integral $Li q\equiv\int_{0}^{q}\frac{dx}{log x}$ , $L^{n}(1+x)\equiv x-\frac{x^{2}}{2^{n}}+\frac{x^{3}}{3^{n}}-&c.$ , Legendre's $X_{n}$       see "Legendre"
Functions, number of values of      C.48
Functions, P, where $\int_{0}^{P}e exp\left(-\frac{x^{2}}{h^{2}}\right)dx=\frac{h\surd\pi}{4}$       Q.10
Functions, Q(x)      Ac.2
Functions, rationally connected      L.59
Functions, representation of      C.923 M.17
Functions, representation of, one-valued      Z.25
Functions, representation of, one-valued, $y=e^{\lambda x^{r}}\lambda$ , constant and r a positive integer      A.42
Functions, representation of, one-valued, $y=x^{n}e^{\lambda x^{2}}$       A.52
Functions, representation of, one-valued, approximate      Z.3
Functions, representation of, one-valued, by an arbitrary curve      M.22
Functions, representation of, one-valued, by Bessel's functions      M.6
Functions, representation of, one-valued, by definite integrals      Ac.2
Functions, representation of, one-valued, by elliptic functions      An.82
Functions, representation of, one-valued, by Euler's sum-formula      J.56
Functions, representation of, one-valued, by Fourier's series      Mo.85
Functions, representation of, one-valued, by graphic methods      A.2
Functions, representation of, one-valued, by graphic methods, imag.      J.55
Functions, representation of, one-valued, by infinite products      Z.24
Functions, reproduced by substitution      C.19
Functions, resolution into factors      Ac.65 C.19 30 CP.11 J.18
Functions, satisfying the eq. $\delta F=0$       C.96
Functions, sine-integral, $Siq\equiv\int_{0}^{q}\frac{sin x}{x}dx$       taP.70
Functions, singularities of      M.19
Functions, systems of      Mo.78
Functions, systems of two interconnected      C.98
Gamma function, $\Gamma(n)$       2284 A.4 6 61 An.69 C.35 92 96 J.35 82 90 ap L.42 46 52 55 Q.9 Z.1 25
Gamma function, $\Gamma(n)$ , application of this and other transcendents      C.86
Gamma function, $\Gamma(n)$ , curve $y=\Gamma(x)$       2323
Gamma function, $\Gamma(n)$ , deductions      2286—2316 A.10
Gamma function, $\Gamma(n)$ , derivatives of      Q.6
Gamma function, $\Gamma(n)$ , logarithm of      2294 2768 C.9
Gamma function, $\Gamma(n)$ , logarithm of, as a definite integral      2768
Gamma function, $\Gamma(n)$ , logarithm of, numerical calculation      2771
Gamma function, $\Gamma(n)$ , n, negative      CD.8
Gamma function, $\Gamma(n)$ , numerical calculation of      2317
Gamma function, $\Gamma(n)$ , of a complex      Me.84
Gamma function, $\Gamma(n)$ , of an infinite product      J.39
Gamma function, $\Gamma(n)$ , of equidifferent products      J.36
Gamma function, $\Gamma(n)$ , reciprocal of      Z.25
Gamma function, $\Gamma(n)$ , reduction of      J.40
Gamma function, $\Gamma(n)$ , the function $\psi(x)\equiv d_{x}log\Gamma(x)$       2743—2770
Gamma function, $\Gamma(n)$ , transformation of      2284 2318 J.57
Gamma function, $\Gamma(n)=limt. of\frac{\mu!\mu_{n}}{n^{\mu+1}}$       2293 A.30
Gauche cubics      C.82 J.60 N.62
Gauche cubics through five points      N.83
Gauche cubics through six points, cn      N.66
Gauche cubics, 3rd class, theorems      J.58
Gauche cubics, number of common chords of two      An.70
Gauche curves      C.70 77 90 Mo.82 thsN.53
Gauche curves of a developable surface, singularities      An.70
Gauche curves of the zero species      C.80
Gauche curves on a cubic surface      C.62
Gauche curves on a one-fold hyperboloid      An.1 C.52 53
Gauche curves, classification of      JP.32
Gauche curves, differential invariants of      JP.28
Gauche curves, intersection of two surfaces having common multiple points, singularities of      C.80
Gauche curves, metric properties of, in linear space of n dimensions      M.19
Gauche curves, representative curve of the surface of principal normal of      C.86
Gauche helicoids in perspective      JP.20
Gauche helicoids, rad. of curv.      N.45
Gauche in-polygons of a quadric      C.82
Gauche, perspective of algebraic curves      C.80
Gauche, projection      N.65
Gauche, quadric      N.67
Gauche, quadric and orthogonal trajectory of generatrices      thN.48
Gauche, quartic      A.62 C.82 L.70
Gauche, quartic, 9 points of, 7 points of a gauche cubic and 8 associated points      C.98
Gauche, quartic, surface      N.61
Gauche, quartic, unicursal, a class of      C.83
Gauche, sextic curve      C.76
Gauche, surface      JP.17 L.37 72
Gauche, surface which can be represented by a p.f.d.e of the 2nd order      C.61
Gauche, surface, deformation of      C.57

Gauss's function      see "Hypergeometric function"
Gauss's theorems      J.3
Gaussian periods of congruent roots corresponding to circle division      J.53
General methods in anal. geometry      4114
General numerical solution of any problem      LM.2
Generating functions      3732 J.81 N.81 Pr.5
Generating functions and ground-forms of binary quantics of first ten orders      AJ.2 3
Generating functions for ternary systems of binary forms, ta      AJ.5
Generating functions of some transcendental series      At.55
Generating functions, do. of binary 12-ic and of irreducible syzygies of certain quantities      AJ.4
Geodesics      5775 5837—5855 A.39 C.40 41 96 p.c CD.5 G.19 J.50 91 M.20 Me.71 N.45 65 Q.1 5 Z.18 26
Geodesics of cubic surfaces, loci      CD.6
Geodesics on a quadric or ellipsoid      C.22 CD.4 J.19 L.4 41 44 48 57 M.35 N.76
Geodesics on a quadric or ellipsoid and corresponding plane curves      C.50
Geodesics on a quadric or ellipsoid and lines of curvature      L.46 N.82
Geodesics on a quadric or ellipsoid through an umbilic      5850
Geodesics on a quadric or ellipsoid, Joachimsthal's theorem      J.42
Geodesics on a quadric or ellipsoid, pd constant along such      5842
Geodesics on a quadric or ellipsoid, shortest lines      J.26
Geodesics on a right cone      A.69
Geodesics on a spheroid      J.43
Geodesics, curvature      5846 C.42 80 L.12
Geodesics, curvature on an ellipsoid      M.20
Geodesics, curvature, radius of      5776 5846
Geodesics, duals of      Q.12
Geodesics, equations of      5837
Geodesics, flexure of      C.66
Geodesics, forms from cn of their polar systems      Z.24
Geodesics, geometry      5855
Geodesics, problems      A.8 An.65 0 J.53 L.49 TN.73
Geodesics, radius of torsion of      5848
Geodesics, radius of torsion of, $RR^{'}P_{2p}+P=0$       Me.75
Geodesics, sections      Z.2
Geodesics, shortest lines on surfaces      5838 J.20
Geodesics, triangles      Mo.82
Geodesics, triangles, best form of      N.55
Geodesics, triangles, reduction of arc of a small one      An.50
Geodesy, spherical problems      A.25 63
Geodesy, spherical problems, representation of one surface upon another      An.70
Geodetica, integration of its eq      An.53
Geography, comparative      A.57
Geometrical and ultra-geometric quantities      C.52 55
Geometrical conics      1150—1292 G.1 Me.62 64 71 73 Q.10 see
Geometrical constructions      LM.2
Geometrical definitions      J.1
Geometrical dissections and transformations      Me.75
Geometrical drawing      A.23
Geometrical figures, general affinity of      J.12
Geometrical forms      G.1
Geometrical forms of 2nd species      G.3 4
Geometrical mean      92 CD.8 Pr.29
Geometrical mean, approx. to by a series of arith. and harm. means      N.79
Geometrical paradoxes      Z.24
Geometrical problems      At.25 32
Geometrical progression      83 A.pr2 6 G.11 N.54
Geometrical progression, a property of 1, 3, 9, 27...      A.33
Geometrical proportion, theory of pure      A.62
Geometrical quantities and algebraic eqs      C.29
Geometrical reckoning (Abzahlenden)      M.10
Geometrical relation of the 5th degree      M.2
Geometrical relations, ap of statics      J.21
Geometrical signs      Z.14
Geometrical theorems      J.11 L.46 N.74
Geometrical theorems and problems      920—1102
Geometrical theorems from a principle in alg.      LM.11
Geometrical theorems, Lawson's      Man.13
Geometrical theorems, method of discovering      J.8
Geometrical transformations      A.32
Geometry and mechanics, on their connection      L.78
Geometry in lieu of proportion      CP.10
Geometry of derivation      An.54
Geometry of masses      JP.21
Geometry of position      J.50 Q.1
Geometry of position, 5 points in space      CM.2
Geometry of position, anal      TE.9
Geometry of position, theorems      An.55 J.31 34 38 41 TE.28
Geometry of space, abstract      Pr.14 18
Geometry of space, abstract, aphorisms      J.24
Geometry of the Ancients      At.22
Geometry of three dimensions      5501—6165 N.63
Geometry, comparative, ap. to conics      N.65
Geometry, der Lage      Z.6
Geometry, elementary      920—1102 J.6 10 A.2 N.62
Geometry, elementary, principles of      A.40 C.56 G.11 14 20 LM.16 Me.62 Z.20
Geometry, enumerative      Ac.1
Geometry, higher      A.20 No.73 prsA.55
Geometry, instinct of construction      N.56 Q.2
Geometry, linear      A.27
Geometry, linear and metrical      M.5
Geometry, linear, ap. to quadrics      M.10
Geometry, organic, of Maclaurin      L.57
Geometry, plane and solid, analogies      L.36 N.65
Geometry, plane and spherical, ths      Mem.15
Geometry, plane, new anal. foundation      M.6
Glissettes centre of curv.      JP.21
Glissettes centre of curv., rad of curv.      L.45
Glissettes problem      Q.11
Golden section      A.4
Goniometrical problems      Q.7 15
Graphic Calculus      C.89
Graphs (Clifford's)      LM.10
Graphs (Clifford's), application to binary quantics      LM.17
Graphs (Clifford's), application to compound partitions      AJ.96
Grassman's life and works      M.14
Greatest common measure      see "Highest common factor"
Greatheed's theorem, D.C      CM.1
Grebe's point      A.58
Green's theorem, &c.      J.39 44 47 TE.26
Griffith's theorem (Conics)      6096
Ground figures, single and double relations      J.88
groups      AJ.1 LM.9 M.13 20 22
Groups of 168 substitutions and septic equations      M.20
Groups of finite order contained in the semi-cubic groups of Cremona      C.99
Groups of finite order, contained in a group of quadratic substitutions      C.97 98
Groups of interchangeable elements      J.86
Groups of many-valued functions      Man.62
Groups of points $G^{'}_{4}$ on a sextic with 5 double points      M.8
Groups of substitutions      C.67 84 94 M.5
Groups of substitutions, isomorphism of      G.16
Groups, $(P)_{360}(\Pi)_{360}$ of the figure of six linear complexes of right lines two and two in involution      An.83
Groups, cyclic, in Cremona's transf. of a plane      An.82
Groups, cyclic, in Cremona's transf. of a plane, in a quadratic transformation      An.82
Groups, discontinuous      C.94
Groups, discontinuous, of linear substitutions      Ac.1
Groups, formed from a finite number of linear substitutions      C.83
Groups, Fuchsian      Ac.1
Groups, introduction to the theory of      Me.62
Groups, Kleinean      C.93
Groups, modular eqs. (Galois)      M.14 18
Groups, non-modular      Man.65
Groups, primitive      C.72 78 96 L.71
Groups, primitive, degree of, containing a given substitution      J.79
Groups, primitive, for the first 16 degrees      C.75
Groups, principal, classification of      C.73
Groups, transitive      G.22 J.83 N.84
Guldin's theorems      5879 Me.85
Harmonic axes of a system of right lines and planes      G.4
Harmonic axes of curves      C.74
Harmonic centre for a system of 4 points in relation to a given pole      Z.20
Harmonic division of a conic      G.10
Harmonic division of a quadric      G.10
Harmonic division of a right line by a circle and chord of contact      948
Harmonic hexhedron and octahedron      Z.18
Harmonic pencils and ranges      933 4649 Q.6
Harmonic pencils and ranges of 4 tangents to two conics, locus of vertex      4984
Harmonic points, system of four      1063 N.51
Harmonic polar curves      A.50 M.2
Harmonic progression or proportion      87
Harmonic progression or proportion, divergency of      A.1
Harmonic progression or proportion, ext of th      A.31 43 tr41 C.43 Me.82 .N.85 Z.3 14

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