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| Hancock H. — Elliptic Integrals |
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| Предметный указатель |
 see Integral \varphi)$"/>
 Tables for 93
, the complete integral 16 17 81
 see Integral F(k h)
 Tables for 93
, the complete integral 16 17 81
 , tables for 93
, the transcendents 26
Abel, Niels 6 7 24 29 31
Addition-theorem 7
Amplitude 24
Andoyer, H. 6
Appell and Lacour, Fonctions Elliptiques 7 14 21
Arithmetico-geometrical mean 78
Bernoulli, Jacob 6 7
Burnside, W. S. 54
Byerly, Integral Calculus 48 63 90 91
Calculation of argument, when k and the function are given 87
Calculation of elliptic function, when modulus and argument are given 87
Calculation of elliptic functions 33
Cayley, Arthur 6 14 16 28 65 68 73 76
Clifford, W. K. 41
Co-amplitude 35
Computation see Numerical computation
Cosine-amplitude =  24
D'Alembert, Jean 6
Delta-amplitude =  24
Durege, Elliptische Funktionen 59
Elastic curves 6 89
Enneper, Elliptische Funktionen 8 10 12
Euler, Leonhard 7
Fagnano, G. C. 6 7
Fricke, Elliptische Funktionen 8
Functions, elliptic 23—39
Gauss, C. F. 78
Graphs of the functions  , and 36 37 38
Graphs of the integrals of the first and second kinds 16 17 18 19 20
Greenhill, A. G. 6 52
Gudermann, M. 24 28
Gudermannian, The 28 29
Hancock, Harris 6 10 15
Hermite, Chas. 6
Humbert, G. 92
Hyperbola, rectification of 6
Infinities 35 36 37 38
Integral, the  15
Integrals of certain elliptic functions 58—63
| Integrals of first kind reduced to normal form 41—63
Integrals, normal 10 15
Integrals, of the first, second and third kinds 9 60
Integrals, tables ior  and 94—101
Integrals, the and , their graphs 15—20
Integrals, the general elliptic 9 14
Jacobi's imaginary transformation 25 34
Jacobi, C. G. J. 5 6 7 24 25 26 29 31 34 65
Lacour, E. see Paul Appell
Lagrange, Joseph L. 7 68
Landen's transformations 65—73
Landen, John 68
Latitude 89
Legendre's transformation 10—13
Legendre, Adrien Marie 5 6 7 9 10 11 12 15 21 22 23 24 61 68 71 81 82 84 92
Lemniscate 7 88
Levy, Fonctions elliptiques 21 92
Maclaurin, Colin 6
Modulus 12
Molk, Jules see Jules Tannery
Numerical computation of integrals of 1st and 2d kinds 69—87
Pendulum, simple 90 91
Period-parallelogram 32
Period-parallelogram of  37
Period-parallelogram of  38
Period-parallelogram of  35
Period-strip 31
Periodic functions, property of 7 31
periods 27 31 35—38
Quadrant of ellipse 89
Quadrant of lemniscate 88
Rectification of ellipse 88
Rectification of lemniscate 88
Reduction formulas 59—61
Richelot, F. S. 10
Serret, J. A. 7
Simpson's Fluxions 91
Sine-amplitude = 24
Tables of complete integrals of 1st and 2d kinds 93
Tables of elliptic integrals of 1st kind 94—97
Tables of elliptic integrals of 2d kind 98—101
Tables of useful integrals 61—63
Tannery and Molk, Fonctions Elliptiques 14
Volume common to two cylinders 89
Wallis's formula 26 60
Weierstrass, Karl 24 28
Zeroes 35—38
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