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Hancock H. — Elliptic Integrals

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Название: Elliptic Integrals

Автор: Hancock H.

Аннотация:

Elliptic integrals can be viewed as generalizations of the inverse trigonometric functions and provide solutions to a wider class of problems. For instance, while the arc length of a circle is given as a simple function of the parameter, computing the arc length of an ellipse requires an elliptic integral. Similarly, the position of a pendulum is given by a trigonometric function as a function of time for small angle oscillations, but the full solution for arbitrarily large displacements requires the use of elliptic integrals. Many other problems in electromagnetism and gravitation are solved by elliptic integrals.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1917

Количество страниц: 105

Добавлена в каталог: 04.03.2013

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Предметный указатель

$E(k, \Phi)$ (see Integral $E(k</a></span> <span class=subjpages><a href=

\Phi)$"/>
$E_{1}$ , the complete integral      16 17 81
$E_{1}$ , the complete integral, Tables for $E_{1}$       93
$F_{1}$ , the complete integral      16 17 81
$F_{1}$ , the complete integral, Tables for $F_{1}$       93
Abel, Niels      6 7 24 29 31
Addition — Theorem      7
Amplitude      24
Andoyer, H.      6
Appell and Lacour, Foncticms 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=cn      24
Delta-amplitude=dn      24
Durege, Elliptische Funktionert      59
d’Alembert, Jean      6
Elastic curves      6 89
Enneper, Elliptische Funktionen      8 10 12
Euler, Leonhard      7
F(k, h)      (see Integral F(k h))
Fagnano, G. C.      6 7
Fricke, Elliptische Funktionen      8
Functions, elliptic      22—39
Gauss, C. F.      78
Graphs of the functions sn, cn and dn      36 37 38
Graphs of the integrals of the first and second kinds      16 17 18 19 20
GreenhiU, A. G.      6 52
Gudermann, M.      24 28
Gudermannian, The      28 29
Hancock, Harris      6 10 15
Humbert, G.      92
Hyperbola, rectification of      6
Ilermite, Chas.      6
Infinities      36 37 38
Integral, the $\Pi(n, k, \Phi)$       4 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 for $F(k, \Phi)$ and $E(k, \Phi)$       94 101
Integrals, the $F(k, \Phi)$ and $E(k, \Phi)$ their graphs      15—20
Integrals, the general elliptic      9 14
Jacobi, C. G- J.      5 6 7 24 25 26 20 31 34 65
Jacobi’s imaginary transformation      25 34
K, K', tables for      93
K, K', the transcendents      26
Lacour, E.      (see Paul Appell)
Lagrange, Joseph L.      7 68
Landen, John      68
Landen’s transformations      65—73
Latitude      89
Legendre, Adrien Marie      5 6 7 9 10
Legendre’s transformation      10—13
Lemniscate      7 88
Levy, Foncltons ellipliques      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 sn u      35
Period-strip      31
Periodic functions, property of      7 31
periods      27 31
Quadrant of ellipse      89
Quadrant of lemniscate      88
Rectification of ellipse      88
Rectification of lemnis-cate      88
Reduction formulas      59—61
Richelot, F. S.      10
Serret, J. A      7
Simpson’s Fluxions      91
Sine-amplitude =sn      24
Tabies 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
Volume common to two cylinders      89
Wallis’s formula      26 60
Weierstrass, Karl      24 28
Zeroes      3

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