Sofo A. — Computational Techniques for the Summation of Series :: Электронная библиотека попечительского совета мехмата МГУ

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Sofo A. — Computational Techniques for the Summation of Series

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Название: Computational Techniques for the Summation of Series

Автор: Sofo A.

Аннотация:

Computational Techniques for the Summation of Series is a text on the representation of series in closed form. The book presents a unified treatment of summation of sums and series using function theoretic methods. A technique is developed based on residue theory that is useful for the summation of series of both Hypergeometric and Non-Hypergeometric type. The theory is supported by a large number of examples. The book is both a blending of continuous and discrete mathematics and, in addition to its theoretical base; it also places many of the examples in an applicable setting. This text is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in mathematics, engineering and related fields.

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Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1

Год издания: 2003

Количество страниц: 701

Добавлена в каталог: 16.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Abel      57 115
Abel type series      39 90
Analytic continuation      70
bernoulli      1
Bernoulli generalised polynomials      11
Bernoulli, $\alpha$ -Bernoulli numbers      11
Bessel functions      7 11 13
beta function      24 54 126 158
binomial      161
Binomial coefficients      14 111 116 118 161
Binomial convolution      116
Binomial expansions      126
Binomial summation      14
Binomial sums      12 117 147
Binomial sums and products      135
Binomial theorem      57
Binomial type series      14
Binomial type sums      73
Binomial variation      147
Bromwich contour      32 89
Bruwier Series      43
Buermann's theorem      x 31 33 36 63 97
Buermann's Theorem, Application      36 67 68
Buermann's Theorem, proof      64—67
Buermann's Theorem, properties      64
Buermann's Theorem, remainder      68 69
Cassini's identity      133
Catalan numbers      118 119
Cauchy      57
Cauchy integral      63 64 67
Cauchy product      11
Cauchy theorem      65
Cebysev      13 125
Central binomial coefficients      111 116 118 161
Characteristic function      31—33 36 38 43 89 104 105 107 112 125 137 147 165 169 170
Combinatorial sums      14
Complex variable      38 64 111 169
Complex zeros      52 53
Conolly's problem      x 32 53 60
Contour integration      3
Convolution      7 92 93 98 116 161
Creative telescoping      26 135 138
Delays      42
Delays, mixed      42
Delays, multiple      32 42
Delays, neutral      42
Difference-delay system      x 111 135
Differential-difference equation      31 32 39 44 45 48 51 87 88
Dirac delta function      5 74 88
Discrete step function      112 136
Divergent      42 71
Divergent series      38
Dominant simple zero      34
Dynamical system      87 99 103 108 160
Euler      1 53
Euler classical polynomials      11
Euler generalization of the Euler Sum      87
Euler result      7
Euler sums      3
Fermat      124
fibonacci      x 111 124
Fibonacci products      123
Fibonacci sequence      123 128 134—136
Finite binomial      x 73 87 135
Forcing terms      40 43 88 99 104 108 136 144 160 174
Functional forms      99 111 124 129
Gauss      8 13 19
Gauss classical formula      19
Gauss hypergeometric series      158
Gauss summation formula      13
Gegenbauer      13
Geometric series      7 12 66 68
Gessel      14 17
Grazing system      x 31 50
Heaviside      32 47 49 74 89
Homogeneous      32 43 135
Hypergeometric closed form representation      12
Hypergeometric connection      14 173
Hypergeometric form      18
Hypergeometric function      3 8 12 26 122 147 157 158 159
Hypergeometric Gauss hypergeometric scries      158 @ !

Hypergeometric series      12 13
Hypergeometric summation      111
Hypergeometric sums      14
Induction      2 90 97 130 147 152 154
Integral equations      4
Inverse Laplace      32 33 88
jacobi      13 56
Jacobi polynomials      24
Jacobsthal      124
Jensen      32 53 55 56 114—116
Jonassen and Knuth      14 16
Lagrange formula      114 115
Lagrange inversion      55
Lagrange theorem      63
Lagrange — Buermann      63
Lambert series      54 128 129
Laplace transform      4 7 31 32 42 74 88 102
Laurent expansion      46
Legendre function      7
Legendre inverse pairs      24
Legendre polynomial      13
Leibniz      1
Leibniz rule of differentiation      92
Lethargy      47
Lord Rayleigh      6 7
Maclaurin series      75 76 82
Mathematica      18 20 21 26—28 142
Mean time to repair      48
Moments      5 92
Multiple zeros      135 138 142
Neutron behaviour      x 31
Newton      1
Newton forward difference formula      168
Numerical estimates      10
Pell      124
Pfaff — Saalschuetz identity      24
Pfaff — Saalschuetz summation      13
Pfaff's reflection law      19
Placzek function      47
Pochhammer      12 54 100 118 150 158
Poisson process      50
Poles      3 33 46 89 137 138 165
Poles, simple      112 167
Polya and Szegoe      38
Polygamma functions      7 9 10
Quadratic transformation      158
Ramanujan      2 57
Rational certificate functional      142 156
Recurrance relation      152
Reed Dawson      16 20—22 26 27
Renewal      31 46 48 103
Renewal process      x 87 102
Residue      3 7 33 47 49 89 90 104 112 137 148 165
Residue theorem      32 89
Residue theory      3
Riordan      14—16 21
Rouche's theorem      105 170 171
Rousseau      14 17
Ruin problem      31 50
Simple function      36 64 67
Sister Celine      14 25 26
Snake Oil Method      21
Steady state      51
Stirling approximation      38 61
Stirling numbers      x 82
Taylor series      6 37 91 121 149 153
Teletraffic      x 31
Transcendental equation      51
Transcendental function      6 31 51 52 109
Tree search      1 14
Triangular matrix      81
Vandermonde identity      23
Volterra integral      73
Wave, rectangular      74 92
Wilf      12 14 21 26 28 116 128 135 138 147 161 173
WZ pairs      14 26 27 135 138 147 156 161 173
Z transform      x 111 112 135—137 165
Zb algorithm      18 20 21 26
Zeilberger      2 12 14 26 135 138 147 161 173
Zeilberger algorithm      24
zeros      6 25 32—34 51—53 89 103—107 109 112 124 137 138 142 148 165—169 172
Zeros, complex      52 53

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