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 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Cayley A. — An elementary treatise on elliptic functions Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: An elementary treatise on elliptic functions Автор: Cayley A. Язык: Рубрика: Математика/Анализ/Специальные функции/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1895 Количество страниц: 386 Добавлена в каталог: 09.04.2005 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель
 Abel, linear and quadric transformations      322 325 375 376 Abel, linear and quadric transformations, irrational transformation      382 Addition      see “Function (2)...(9)” Arc of curve, determination of curves the arc of which represents elliptic integral of first kind      352 (Chap. xv.) Arc of curve, representing integrals , (ellipse, hyperbola, lemniscate)      35 Arithmetico-geometrical mean      332 Baehr’s formuls for multiplication of sn, en, dn      79 Circular functions, illustration by reference to      10 Definitions and Notations      1 (Chap. I.) Definitions and Notations, amplitude, modulus, complementary modulus, parameter      3 Definitions and Notations, complete functions , 4 Definitions and Notations, elliptic functions am, sin am, cos am, am, or sn, en, dn      8 Definitions and Notations, elliptic integrals , , 3 Definitions and Notations, Eu, Zu, 15 Definitions and Notations, K, K'      12 Definitions and Notations, \Theta u\$, Hu      16 Differential equation of third order, satisfied by modulus in transformation of nth order      222 Differential equation, addition-equation      5 21 Differential equation, equation 339 (Chap XIV.) Differential equation, partial, satisfied by , H, &c, and the numerators and denominators in multiplication and transformation of sn, en, dn      226 (Chap. IX.). Differential equation, satisfied by , , or by , 47 50 Differential equation, satisfied by multiplier      220 Differential equation, special equation      250 Dimidiation      72 see Doubly infinite products      see “Factorial” Duplication      71 see Duplication by two quadratic transformations      181 Euler, partition formula      290 Factorial formule      92 97 Factorial formule, doubly infinite product forms      101 300 Function, (1), reduction to standard form 1      311 (Chap. xii.) Function, (10), , Hu      142 (Ch. VI.) 226 Function, (10), , h expressed as q-functions      291 Function, (10), connexion with sn, en, dn, Zu and 155 Function, (10), development in q-series      297 Function, (10), double factorial expressions      300 Function, (10), Hu introduced      156 Function, (10), multiplication      159 Function, (10), partial differential equations      229 Function, (10), properties of 150 152 Function, (10), transformation      306 Function, (11), connexion with , Hu      161 Function, (11), connexion with functions , H      309 Function, (11), numerators and denominator in multiplication and transformation of sn, en, dn      226 (Chap. rx.) Function, (11), partial differential equations      235 Function, (11), verification for cubic transformation      245 Function, (12), , H expressed as q-formulae      291 Function, (12), derivation of the q-formulas      282 Function, (12), q-functions      282 (Chap. xi.) Function, (13), further theory      342 Function, (13), Lagrange’s integration      339 Function, (13), The general equation 339 (Chap. XIV.) Function, (2), addition - equation 21 (Chap. II.) Function, (3), , march of function      41 Function, (3), addition      103 Function, (3), imaginary modulus 367 Function, (3), properties as function of k      46 Function, (3), quadric transformation, &c      327 Function, (4), 41 (see also “Infra march Function, (4), addition      104 Function, (4), properties as function of k      46 Function, (4), quadric transformation, &c      327 Function, (5), see also “(9) infra” Function, (5), addition      104 Function, (5), addition of parameters, and reduction to standard form      117 Function, (5), interchange of amplitude and parameter      133 Function, (5), outline of further theory      108 Function, (5), reduction of parameter to form 114 Function, (6), gd u, sg u, eg u., addition and other properties      56 Function, (7), addition and subtraction formulae      63 Function, (7), anticipation of doubly infinite product forms      101 Function, (7), connexion with , Hu      155 156 Function, (7), dimidiation      72 Function, (7), duplication      71 Function, (7), factorial formulae      92 Function, (7), functions of u + (0, 1, 2, 3) K + (0, 1, 2, 3) iK'      69 Function, (7), imaginary transformation      68 Function, (7), multiplication      78 Function, (7), n-thic transformation      251 (Ch. x.). Function, (7), new form of same      97 Function, (7), periods 4K, 4iK'      66 Function, (7), quadric transformations      183 Function, (7), sn u, en u, dn u      63 (Chap. IV.) Function, (7), triplication      77 Function, (8), addition      107 Function, (8), connexion with 113 Function, (8), Em, Zu, connexion with 107 Function, (8), further theory      147 Function, (9), 142 (Chap. VI.). Function, (9), expressed in terms of Qu      151 Function, (9), addition of amplitudes      157 Function, (9), addition of parameters      157 Function, (9), connexion with 107 Function, (9), connexion with 6m      113 Function, (9), interchange of amplitude and parameter      159 Function, (9), values of for 144 Gauss, the arithmetico - geometrical mean      331 338 Glaisher, proof of Legendre’s relation between complete functions , &c      49 Glaisher, tables of theta functions      155 Gordan, integral reducible to elliptic functions      369 Gudermann      44 58 Gudermannian      58 (see also “Function (6)”) Imaginary transformation, Jacobi’s      68 Imaginary, reduction of given, to form 114 Integrals involving root of a quintic function and reducible to elliptic integrals      360 (Chap. XVI.) Integrals involving root of a quintic function and reducible to elliptic integrals, involving root of a sextic function      369 Integration, general theorem of      354 jacobi      16 18 19 23 28 66 150 176 220 223 224 227 323 Kummer, formula in hypergeometric series      55 Lagrange, integration of differential equation 339 Landen’s theorem      30 327 Legendre, his relation between complete functions, , , , , formula relating to third kind of elliptic integral      119 121 134 Legendre, proof of addition-equation by spherical triangle      27 Legendre, reduction of differential expression to standard form      314 Liouville, formula for arc of curve      40 Modular equation or relations, cubic transformation      188 195 206 Modular equation or relations, linear transformation      322 Modular equation or relations, odd-prime transformation      45 200 275 278 Modular equation or relations, quadric transformation      45 179 Modular equation or relations, quintic transformation      192 195 Modular equation or relations, septic transformation      194 Modular equation, differential equation of third order satisfied by the transformed modulus      222 Modular equation, properties of      200 Modular equation, verification for quadric transformation      223 Multiplication from two transformations      201 280 Multiplication of sn, en, dn      78 86 Multiplication tables      80 81 Multiplier in cubic, &c. transformations      203 Multiplier, differential equation satisfied by      220 Multiplier, Jacobi’s relation 218 Multiplier, relation between M, K, , E, G      224 Notation explained      5 Numerical instance for complete functions , , and for incomplete F      337 Richelot, representation of given imaginary quantity in form 117 Roberts, M., integral reducible to elliptic functions      369 Serret, formula for arc of curve      40 Tables of the theta functions      155 Transformation of functions, H, 306 Transformation, combined, and irrational      379 Transformation, cubic      188 195 206 216 245 Transformation, general outline      164 (Chap. VII.) Transformation, Landen’s theorem      30 327 Transformation, linear transformation of integral      312 319 370 Transformation, multiplication formulae obtained from two transformations      280 Transformation, odd or odd-prime, by the n-division of the complete functions      251 (Chap. x.) Transformation, quadric      179 (Chap viii.) 323 376 Transformation, quintic      191 197 Transformation, septic      194 Transformation, two transformations leading to multiplication      201 Triplication      77 (see also “Function (7)”) Walton, proof of addition-equation      22 Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2021 | | О проекте