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Slater L.J. — Generalized hypergeometric functions
Slater L.J. — Generalized hypergeometric functions

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Название: Generalized hypergeometric functions

Автор: Slater L.J.

Язык: en

Рубрика: Математика/Анализ/Специальные функции/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1966

Количество страниц: 273

Добавлена в каталог: 06.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel's theorem      58
Analytic continuation of Gauss functions      32
Analytic continuation of hypergeometric functions      114
Associated series      14
Associated transformations      14
Asymptotic series, basic analogue      117
Asymptotic series, extensions of Orr's thoorem      77
Asymptotic series, Gauss's      137
Asymptotic series, generalized hypergeometric      146
Bailey's theorem      58
Bailey's theorem, basic analogue      98
Bailey's theorem, partial summation      81
Barnes type contour integrals      109
Barnes type contour integrals, basic analogue of      161
Barnes type contour integrals, Gauss theorem      22
Barnes type contour integrals, general theorems for      130
Basic series, analogue of Dixon's theorem      96
Basic series, analogue of Dougall's theorem      94
Basic series, analogue of Gauss's theorem      97
Basic series, analogue of Saalschutz's theorem      96
Basic series, analogue of Vandermonde's theorem      97
Basic series, convergence of      87
Basic series, functions expressed as      86
Basic series, Gauss analogue      97
Basic series, general transformation theory for      98
Basic series, Heine series for      87
Basic series, inversion of base in      88
Basic series, notations for      88
Basic series, numbers in      106
Basic series, parameters in      90
Basic series, transformation by basic integrals      164
Basic series, well-poised transformations for      169
Bessel functions      47
Beta functions      32
Bilateral series      180
Bilateral series, basic analogue of      190
Binomial theorem      17
Borel contours      27
Borel contours, integrals      26
Cauchy values      25
Cayley's product      79
Clausen's theorem      75
Confluent hypergeometric functions      19
Contents      vii
Contiguous functions      13
Contiguous functions, Gauss series      14
Contiguous functions, generalized      45
Continuous fractions      15
Contour integrals, Barnes type      109
Contour integrals, basic analogue of      161
Contour integrals, Borel type      26
Contour integrals, Pochammer's      22
Convergence of basic series      87
Convergence of bilateral series      181
Convergence of generalized hypergeometric series      45
Coulomb functions      19
D'Alambert's test      4
de l'Hospital's limit      85
Differential equations      42
Differential equations, Gauss equation      5
Differential equations, operators in      43
Differential equations, Riemann's      6
Differential equations, singularities in      5
Differential equations, special cases in      17
Differentiation of Gauss functions      15
Differentiation of general functions      42
Divergence of series      45
Dixon's theorem      51
Dixon's theorem, extension to infinite series      52
Double series, convergence of      211
Dougall's theorem      55
Dougall's theorem, contour integral analogue for      114
Dougall's theorem, extension to infinite series      114
Dougall's theorem, Jackson's basic analogue for      94
Dougall's theorem, proof by induction      55
Dougall's theorem, special cases of      57
Dougall's theorem, transformations based on      67
E-functions      42
Elliptic functions      91
Elliptic modular functions      87
Equivalent products      203
Erdelyi's notations      41
Error functions      19
Euler identities      85
Euler identities, integrals      44
Euler identities, partition functions      85
Euler identities, series      1
Euler identities, theorem      85
Euler identities, transformations      10
Even and odd products      93
Frobenius's process      43
Fuchian equations      42
G-functions      42
Gauss equation, twenty-four solutions of      32
Gauss function, analytic continuation of      35
Gauss function, definition of      1
Gauss function, history of      2
Gauss function, integrals for      19
Gauss function, notations for      4
Gauss function, numerical evaluation of      38
Gauss function, quadratic transform of      49
Gauss second summation theorem      31
Gauss series, convergence of      3
Gauss theorem      27
Gauss theorem, basic analogue of      97
Gauss theorem, integral version of      109
Gauss theorem, symmetry in proof of      28
Gauss, basic analogue of his theorem      97
Gegenbaur functions      18
Gegenbaur functions, polynomials      18
Generalized hypergeometric function      see hypergeometric function generalized
Geometric series      1
Heine's basic series      85
Heine's basic series, convergence of      87
Heine's basic series, definition of      85
Heine's basic series, inversion of base of      88
Hill's theorem      80
Hospital's limit      see de l'Hospital's limit
Hyperbolic functions      17
Hypergeometric functions, definitions of      1
Hypergeometric functions, generalized, contracted notations      40
Hypergeometric functions, generalized, definitions      41
Hypergeometric functions, generalized, differential equations for      42
Hypergeometric functions, generalized, general transformations of      58
Hypergeometric functions, generalized, history of      41
Hypergeometric functions, generalized, integrals for      108
Hypergeometric functions, generalized, integration of      44
Hypergeometric functions, generalized, notations for      42
Hypergeometric functions, generalized, products of      128
Hypergeometric functions, generalized, series for      41
Hypergeometric functions, history of      1
Hypergeometric functions, integrals for      19
Hypergeometric functions, notations for      4
Hypergeometric functions, series for      1
Indicial equation      43
Infinite products, connection with Gamma functions      90
Infinite products, evaluation of      106
Infinite products, notations for      88
Infinite products, tables of      249
Infinite series      1
Integral analogues of Gauss's theorem      109
Integral equations      138
Integrals, Barnes type      162
Integrals, basic analogues of      161
Integrals, contours for      162
Integrals, double      225
Integrals, Euler's      3
Integrals, of generalized hypergeometric functions      44
Integrals, Pincherle's      3
Integrals, Pochammer's      22
Integrals, triple      108
Jackson's theorem      94
Jacobi's theorem      86
Jacobi's theta functions      86
Kummer's equation, definitions      4
Kummer's equation, twenty-four solutions for      8
Kummer's functions      8
Kummer's quadratic transform      49
Kummer's series      31
Kummer's theorem      32
Legendre functions      17
Legendre functions, polynomials      18
Logarithmic solutions      10
MacRobert's E-functions      42
Maijer's G-functions      42
Multinomial theorems      2
Murphy's formula      18
Nearly-poised series      42
Nearly-poised series, basic series      94
Nearly-poised series, definition of      42
Nearly-poised series, first and second kinds      42
Nearly-poised series, summation theorems for      65
Nearly-poised series, transformations of      62
Notations, basic series      89
Notations, gamma functions      41
Notations, Gauss series      4
Notations, hypergeometric series      40
Notations, infinite products      90
Notations, theta functions      86
Operators in differential equations      43
Orr's theorems      75
Papperitz's equation      7
Partial sums of hypergeometric series      80
Partition functions      85
Pincherle      3
Pochammer's contour integral      22
Poles of Gauss's function      6
Poles of generalized function      43
Poole's equation      42
Preface      xii
Products, infinite      90
Products, of Gauss functions      75
Products, of generalized functions      128
Products, q-difference equations      87
Products, q-series      85
Raabe's test      5
Radius of convergence      5
Ramanujan      103
Recurrence relations for Gauss functions      13
Reimann's equation      7
Reimann's P-functions      4
Reversal of series      47
Rodriguez's formula      18
Rogers — Ramanujan identities      103
Rogers — Ramanujan identities, Watson's proof of      105
Saalschutz's theorem      48
Saalschutzian series, basic analogue of      96
Saalschutzian series, integral analogue of      112
Saalschutzian series, summation theorem for      48
Saalschutzian series, transformations of      60
Sears's well-poised theorems      134
Singularities, irregular      42
Singularities, regular      43
Slater's general transformation      143
Slater's partial summation theorem      83
Symmetry in the Gauss functions      27
Tannery's theorem      164
Theta functions      197
Trigonometric functions      17
Vandermonde's basic analogues      97
Vandermonde's theorem      28
Vandermonde's transformations based on      64
Watson's analogue of Whipple's theorem      100
Watson's theorem      54
Well-poised series, basic analogues of      101
Well-poised series, contour integrals for      112
Well-poised series, definitions      42
Well-poised series, integrals of      134
Well-poised series, summation theorems of      55
Well-poised series, transformations based on      13
Whipple's theorem      10
Whipple's transforms      115
Whittaker's functions      19
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