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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Residues, ap. to integrals whose derivatives involve the roots of alg. eqs.      C.23
Residues, ap. to reciprocity law of two primes and asymptotes      C.76
Residues, biquadratic      C.64 J.28 39 L.67
Residues, cubic      A.43 63 C.79 J.28 32 L.76
Residues, quadratic      Ac.1 J.28 71 Q.1
Residues, quadratic and partition of numbers      J.61
Residues, quadratic of primes, also non-residues      L.42 Mel.4
Residues, quadratic, ext. of Gauss's criticism      Mo.76
Residues, quintic      C.76 Z.27
Residues, septic      C.80
Resultant alg.      M.16 extC.58
Resultant alg. and discriminants and product of differences of roots of eqs., relation      Me.80
Resultant alg. of 3 ternary quadrics      J.57 N.69
Resultant alg. of covariants      M.4
Resultant alg. of n equations      An.56
Resultant alg. of two equations      J.30 50 53 54 M.3 P.57 68
Resultant alg. of two integral functions      Z.17
Reversible symbolic factors      Q.9
Reversion of angles      LM.6
Rhizic curves      Q.11
Rhombus, circumscribing an equil. triangle      A.45
Rhombus, quadrisection by two rectangular lines      Mem.11
Riemann's function      A.68 J.83 M.21
Riemann's function, $\theta$ -formula, gz      Ac.3
Riemann's function, ext. to hyper-geo.-functions of 2 variables      C.95
Riemann's surface      LM.8 M.6 18 thsZ.12
Riemann's surface of 3rd species      M.17
Riemann's surface, irrationality of      M.17
Riemann's surface, new kind of      M.7 10
Right cone      Me.72 73 75 76
Right line      A.49 57 fQ.15 t.c
Right line and circle      ths N.56
Right line and conic      Q.7
Right line and conic, cn. for points of section      A.59 66 N.85
Right line and conic, condition of touching      4315 4323 t.c
Right line and conic, quadratic for abscissae of the points      4319
Right line and conic, tg.e of the points      4903
Right line and curve      4131—4135
Right line and curve, a constant product      C.82 83
Right line and curve, a constant ratio      C.83
Right line and curve, ths. in which pairs of segments have a constant length      C.83
Right line and curve, ths. in which systems of 3 segments have a constant product      C.83
Right line and plane      prs CD.1 CM.2 t.c q.c
Right line and quadric      5676
Right line and quadric of revolution      N.82
Right line and quadric, harmonic division      5687
Right line at infinity      4612—4614 tg.c
Right line at infinity, cond. for touching a curve      4900
Right line through a point      4073 4088—4089 4099 t.c
Right line through a point and perp. or paral. to a given line      sd5538—5539
Right line through a point, condition      4101
Right line through four lines in space      A.1 CM.3
Right line through four lines in space, Gergonne's pr.      J.2 N.17
Right line through two points      4083 sd5537 t.c 4789 p.c
Right line through two points on a conic, equation of, ellipse      4324
Right line through two points on a conic, equation of, parab.      4225
Right line under four given conditions      C.68
Right line under given conditions      C.73 74
Right line, constants, relations between      sd. 5515
Right line, coordinates of      G.10
Right line, coordinates of, relation between two      4897
Right line, crystallography      A.34
Right line, drawn from x'y' across a conic, gen. eq.      4494
Right line, drawn from x'y' across a conic, method      4134
Right line, drawn from x'y' across a conic, quadratic for the segments in a parabola      4221
Right line, drawn from x'y' across a conic, quadratic for the segments in an ellipse      4314
Right line, equations of      4052—4066 p.c t.c sd q.c
Right line, geometry of      A.64 thsJ.8
Right line, joining two points and crossing a conic, gn.eq.      4487 t.c
Right line, joining two points and crossing a conic, method      4131
Right line, joining two points and crossing a conic, quadratic for ratio of segments in a parabola      4214
Right line, joining two points and crossing a conic, quadratic for ratio of segments in an ellipse      4310
Right line, joining two points, coordinates of point dividing the distance in a given ratio      4032 t.c 5507
Right line, joining two points, coordinates of point dividing the distance in a given ratio, tg.eq. of the point      4879
Right line, pencils of      C.70 L.72
Right line, pencils of, quadruple      J.67
Right line, planes or points through or on given points, lines, or planes, number of such      Z.6
Right line, pole of      t.c 4671 tg.e
Right line, six coordinates of      CP.11
Right line, system of      At.68 G.9 10 16
Right line, system of, and planes, geo. of 2nd kind      At.65
Right line, system of, in space      G.11 12 L.46
Right line, system of, of 1st degree      G.6
Right line, system of, of 2nd degree      G.7
Right line, three points lying on, cond.      4036 t.c
Right line, three, condition of intersection      4097 t.c
Right line, touching a surface, condition      5786
Right line, touching a surface, quadric      5703
Right line, two, bisector of the angle      4113 sd5540 q.c
Right line, two, cond. of either touching the conic      4964
Right line, two, cond. of intersecting on a conic, gn.eq      4962
Right line, two, cond. of intersection      sd5533
Right line, two, cond. of parallelism      4076 t.c sd5531
Right line, two, cond. of perp.      4078 t.c sd5532
Right line, two, coordinates      4090 t.c
Right line, two, drawn to the points of section of a right line and conic, eq. of      A.69
Right line, two, right angle between them      4112 sd5520 5553 CP.2 N.66
Right line, two, shortest distance      sd5534—5536
Right line, two, through origin, eq. of      4111
Right solid, M. I. of      6018 thA.34
Right-angled triangles      718 prs
Right-angled triangles with commensurable sides      E.33
Rodrique's th.      Me.80 84
Rolling and sliding solids, geo      thsC.46
Rolling cones      L.53
Roots of algebraic fractions      N.46
Roots of an equation      50 402 A.14 CM.2 CP.8 E.36 J.20 31 N.42 56 P.1798 37 64 Q.1 5 6 see
Roots of an equation as continued fractions      CM.3
Roots of an equation as definite integrals      J.2
Roots of an equation as definite integrals, $y^{n} - xy^{n - 1} - 1 = 0$       Me.81 P.64
Roots of an equation as determinants of the coefficients      A.59 61
Roots of an equation as functions of a variable parameter      C.30
Roots of an equation in a converging series      C.23 38
Roots of an equation in a given ratio      J.10
Roots of an equation in g.p      N.89
Roots of an equation in sums of rational functions of the coefficients      Ac.6
Roots of an equation of a biquadratic, cn      N.44
Roots of an equation of a biquadratic, cn by parab. and circle      N.87
Roots of an equation of a quadratic      50—53
Roots of an equation of a quartic and of a Hessian, relation      E.34
Roots of an equation of cubic      L.44 N.42
Roots of an equation of cubic and biquadratic      An.55 L.55
Roots of an equation of quintics      C.59 60 LM.14 TI.18
Roots of an equation of the form $a + \surd b + \surd c +$       N.45
Roots of an equation which are the binary products of the roots of two eqs.      An.79
Roots of an equation which satisfies a linear d.e of 2nd order      C.94
Roots of an equation with a variable parameter      C.12
Roots of an equation with equal differences      G.15
Roots of an equation, commensurable      502 N.45 th57
Roots of an equation, commensurable, limits to the number      N.59
Roots of an equation, common      462 C.80 88 N.55 69
Roots of an equation, continuity of      N.76
Roots of an equation, discrimination of      409 A.46
Roots of an equation, do. of differences of roots      C.98
Roots of an equation, do. of the common roots of two eqs.      N.60 Z.15
Roots of an equation, equal      432—447 CD.5 E.33 Mel.1 P.1782 Q.9 18
Roots of an equation, existence of      A.15 CD.2 CP.10 E.36 G.2 J.5 44 88 LM.1 Q.11 TI.26
Roots of an equation, expanded in power series      J.48
Roots of an equation, forms for quadrics, cubics, and quartics      Z.24
Roots of an equation, functions of the roots of another eq.      425 430
Roots of an equation, functions of the roots of another eq., ap      N.50 E.40
Roots of an equation, functions of the roots of another eq., products in pairs      Q.13
Roots of an equation, functions of the roots of another eq., squares of differences      541
Roots of an equation, functions of, relation to coefficients      TE.28
Roots of an equation, functions of, similar      L.54
Roots of an equation, geo.cn of      JP.10
Roots of an equation, imaginary      408
Roots of an equation, imaginary, approx.      N.45 53 Q.9
Roots of an equation, imaginary, between given limits      A.21 L.44
Roots of an equation, imaginary, geo.cn      A.15 45 C.24 86—88 JP.11 L.50 N.46 47 68

Roots of an equation, imaginary, Newton — Fourier rule      Q.16
Roots of an equation, imaginary, Newton — Sylvester rule      530 C.99 LM.1 Me.66 Pr.14 Q.9 TI.24
Roots of an equation, imaginary, Newton's rule      Me.80 N.67 Pr.13
Roots of an equation, in infinite series      A.69
Roots of an equation, incommensurable      506 see
Roots of an equation, infinite      N.44 45
Roots of an equation, integral, by Newton's method of divisors      459
Roots of an equation, least      M.9 TE.28
Roots of an equation, limits of      448 C.58 60 93
Roots of an equation, limits of, geo      CP.12 N.43 45 59 72 80 81
Roots of an equation, limits of, number between given limits      A.1 G.9 J.52 L.40
Roots of an equation, limits of, Rolle's th.      454 AJ.4 N.44
Roots of an equation, limits of, Rolle's th., ext      L.64
Roots of an equation, limits of, Rolle, Fourier, and Descartes      A.1
Roots of an equation, limits of, the eq. containing only odd powers of x      N.63
Roots of an equation, number satisfying a given condition      C.40
Roots of an equation, product of differences      Me.80 P.61
Roots of an equation, rationalization of      P.1798 14
Roots of an equation, real      A.36 58 C.61 J.50 JP.10 N.50 P.57
Roots of an equation, real, developed in a series      L.78 N.56
Roots of an equation, real, Fourier's th.      N.44
Roots of an equation, real, limits of      J.1 N.53 79
Roots of an equation, real, of a cubic      N.72 Z.2
Roots of an equation, real, series which give the number of      Z.2
Roots of an equation, real, to find four      An.55
Roots of an equation, rule of signs      416—423 A.34 C.92 98 99 N.43 46 47 67 69 79
Roots of an equation, separation of      A.28 70 J.20 N.68 72 74 75 80
Roots of an equation, separation of, by differences      N.54
Roots of an equation, separation of, for biquadratics      A.47
Roots of an equation, separation of, for numerical      C.89 92 G.6
Roots of an equation, simultaneous eqs.      C.5
Roots of an equation, squares of differences      541 CM.1 N.42 44 Q.4
Roots of an equation, sums of powers      534 E.38 thJ.9 N.53 75 gzMe.85 Q.19
Roots of an equation, surd forms of      CM.3
Roots of an equation, symmetrical functions of      534 A.16 AJ.1 An.54 55 60 C.44 45 G.5 11 J.19 54 81 Me.81 N.48 50 55 66 84 P.57 Pr.8 Q.4 TI.25
Roots of numbers      108 A.17 26 35 C.58 E.36 Me.75 N.61 70
Roots of numbers as a continued fraction      195 A.6 12 49 CM.2 L.47 Me.85 Mem.10 TE.5 Z.17
Roots of numbers as a continued fraction to 25 decimal places      Me.77
Roots of numbers, cube root and sq. root, limit of error      N.48
Roots of numbers, cube root of 2 to 28 decimal places      Me.76 78
Roots of numbers, cube root, Horner's method      37 A.67
Roots of numbers, fourth root      A.30
Roots of numbers, nth root as a fraction      A.46
Roots of numbers, square root      35 C.93 N.45 46 61 70
Roots of unity      475—481 C.38 J.40 L.38 54 59 Me.75 N.43 TE.21 Z.22
Roots of unity, 23 roots, composition of number      47 J.55 56
Roots of unity, cubic roots, alg. and geo. deductions      C.84
Roots of unity, function theory      Z.22
Rosettes      N.48
Rotation      CM.3 LM.3
Rotation of system of lines drawn through points on a directrix, modulus of      C.21
Rotation, infinitesimal      C.78
Roulettes      5229 Ac.63 C.70 CP.7 J.65 L.80 81 N.56 TE.16 Z.28
Roulettes, areas of, and Steiner's transf.      E.35
Roulettes, generated by a circle rolling on a circle      JP.21
Roulettes, generated by centre of curvature of rolling curve      L.59
Roulettes, generated by focus of ellipse rolling on a right line      A.48
Ruled surfaces      An.68 CD.8 G.3 J.8 L.78 N.61
Ruled surfaces and guiding curve      A.18
Ruled surfaces of minimum area      L.42
Ruled surfaces of species, p = 0      M.5
Ruled surfaces, areas of parallel sections      Z.20
Ruled surfaces, octic with 4 double conics      C.60
Ruled surfaces, P. D. eq. of      Me.77
Ruled surfaces, quadric      Me.68
Ruled surfaces, quartic      A.65
Ruled surfaces, quartic with 2 double lines      A.65
Ruled surfaces, quintic      J.67
Ruled surfaces, represented on a plane      C.85
Ruled surfaces, symm. tetrahedral      C.62
Ruled surfaces, torsal line      M.17
Ruled surfaces, transformation of      C.88
Scales of notation      342 J.1 L.48 5ry 10ry 20ry
Screws      TI.25
Scrolls      A.53 CD.7 CP.11 J.20 67 M.8
Scrolls, condensation of      LM.13
Scrolls, cubic      M.1 P.63 64 69 Pr.12 13 16 Z.cn28
Scrolls, cubic on a quadric surface      Me.85
Scrolls, flexure and equilib. of      LM.12
Scrolls, ruled      A.68
Scrolls, ruled, $z = mxy^{2}$       A.55
Scrolls, tangent curves of      M.12
Sections of the cone      1150
Sectors and segments of conics and conicoids      6019—6162 G.1 thsZ.1
Secular eq. has real roots      J.88
Self-conjugate triangle      4755 4967 G.8 N.67 Q.5 10
Self-conjugate triangle and tetrahedron in conics and quadrics      Z.6
Self-conjugate triangle of 2 conics      Me.77
Self-conjugate triangle of 3 conics      5025
Self-enveloping curves and surfaces      Z.22
Self-reciprocal surface      Mo.78
Self-reciprocal triangle      1020
Seminvariants      AJ.7 E.th42 6 Q.19—21
Seminvariants, critical and Spencian functions      Q.4 6
Seminvariants, critical and symm. functions      AJ.6
Septic equations      Mo.58
Series      125—129 149—159 248—295 756—817 1460 1471—1472 1500—1573 2708—2709 2743—2760 2852—2864 2880 2911—2968 3781 3820 A.4 5 9 14 18 23 60 No.39 47 C.29 pr92 CP.9 G.10 J.3 17 34 38 th53 L.th56 81 Me.64 N.59 th62 70 Q.3 Z.15 16 23 see "Expansions"
Series and definite integrals      L.82 Man.46
Series and differentiations      A.10 J.36
Series from $\int x (1 - x)^{n} dx$       A.47
Series from $\int_{0}^{\frac{\pi}{2}} \cos^{2} x \log \frac{1 + \sin x}{1 - \sin x} dx$       G.10
Series from infinite products      Me.73
Series from log (1 + x), $(1 + x)^{n}$ and $e^{x}$ by intermitting terms in the expansions      A.21
Series in a triangle problem      A.64
Series in a.p      see "Arithmetical progression"
Series in a.p, analogous series      N.69
Series in cosines of multiple angles      C.44 Mem.15
Series in Legendre's function $X_{n}$       An.76 C.44
Series in theory of numbers      C.89
Series of Abel      C.93 N.85
Series of fractions      L.40
Series of Gauss and Heine      C.73 G.9
Series of Hermite, a th.      E.29
Series of Lagrange      C.23 34 52 L.57 N.76 gz85 Q.2
Series of Lagrange, an analogous series      C.99
Series of Lagrange, remainder      C.53
Series of Lambert, $\sum \frac{x^{n}}{1 - x^{n}}$       A.10 An.68 J.9 Z.6
Series of Laplace's functions, $\sum nY_{n}$       C.44
Series of Laplace's functions, $\sum Y_{n}$       C.88
Series of Leibnitz      J.89
Series of odd numbers      A.64
Series of polynomials      C.96
Series of posterns      G.6
Series of powers      277 C.87 G.2 see
Series of powers in a convergent cycle, constants in      M.25
Series of powers of a binomial      Mem.13
Series of powers of terms in ar.p      L.46
Series of powers or multiples of 3      A.27
Series of powers, approximate fractions      J.90
Series of powers, cubes      L.64 65 M.23 Mo.78 Q.8 Z.1
Series of powers, like numbers      N.71 77
Series of reciprocals      Q.8
Series of Schwab      N.59
Series of spherical functions      An.75
Series of Sterling, for transformation      J.59
Series whose coefficients are the sums of divisors of the exponents, sq. of this series      Me.85
Series whose terms are the coefficients of the same power of a single variable in a multiple integral      C.20
Series with Bernoulli's nos.      An.53
Series with Bernoulli's nos. and binomial coefficients      A.23
Series with constant ultimate differences      Pr.52
Series with terms alternately positive and negative      C.64
Series, $1 + \frac{(q^{\alpha} - 1) (q^{\beta} - 1)}{(q - 1) (q^{\gamma} - 1)} x + \frac{(q^{\alpha} - 1) (q^{\alpha + 1} - 1) (q^{\beta} - 1) (q^{\beta + 1} - 1)}{(q - 1) (q^{2} - 1) (q^{\gamma} - 1) (q^{\gamma + 1} - 1)} x^{2} + ...$       J.32 70
Series, $1 + \frac{a}{b} x + \frac{a (a + 1)}{b (b + 1)} x_{2} + ...$       J.37
Series, $1 + \frac{a}{b} x + \frac{a (a + 1)}{b (b + 1)} x_{2} + ...$ with x = 1      J.2
Series, $1 - \frac{n - 3}{2} + \frac{(n - 4) (n - 5)}{2.3} - ...$       J.20
Series, $1 \pm \frac{1}{2^{n}} + \frac{1}{3^{n}} \pm ...$ and $1 \pm \frac{1}{3^{n}} + \frac{1}{5^{n}} \pm$       2940—2944 A.41 LM.8 Q.7
Series, $1 \pm \frac{1}{2^{n}} + \frac{1}{3^{n}} \pm ...$ and $1 \pm \frac{1}{3^{n}} + \frac{1}{5^{n}} \pm$ with n = 1, 2...8      2945 E.32 39 G.10 N.79 Z.3
Series, $1 \pm \frac{1}{2^{n}} + \frac{1}{3^{n}} \pm ...$ and $1 \pm \frac{1}{3^{n}} + \frac{1}{5^{n}} \pm$ , Note that $1 - \frac{1}{3^{2}} + \frac{1}{5^{2}} - \& c. = -\int_{0}^{1} \frac{\log x}{1 + x^{2}} dx$       2391
Series, $1^{p} + 2^{p} + ... + n^{p}$       2939 A.65 Me.78
Series, $1^{p} + 2^{p} + ... + n^{p}$ , p = 1, 2, 3, or 4      276 A.64 E.34

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