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Koepf W. — Hypergeometric Summation. An algorithmic approach to summation and special function identities.
Koepf W. — Hypergeometric Summation. An algorithmic approach to summation and special function identities.

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Название: Hypergeometric Summation. An algorithmic approach to summation and special function identities.

Автор: Koepf W.

Язык: en

Рубрика: Математика/Алгебра/Вычислительная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 230

Добавлена в каталог: 05.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
'recursion/compare'      162
'sumdelta+nabla'(F,k,s(x))      116
(m,l)-fold hypergeometric term      129
A priori bound      52 69 110
Abramowitz functions      203
Admissible hypergeometric term      137
Airy functions      205
Airy integral      205
Algorithm, Almkvist — Zeilberger      183 194
Algorithm, continuous Gosper      183
Algorithm, extended_gosper      125
Algorithm, Fasenmyer      47
Algorithm, Gosper      61
Algorithm, Petkovsek      140
Algorithm, q-differential equations      177
Algorithm, q-Gosper      75
Algorithm, q-Petkovsek      158
Algorithm, q-Zeilberger      113
Algorithm, Risch      61 192
Algorithm, Risch — Bronstein      183 193
Algorithm, simpcomb      15
Algorithm, Zeilberger      93 103
Almkvist — Zeilberger algorithm      183 194
Andrews' identity      127
Antidifference      61
Antidifference, m-fold      124
Apery numbers      29 101 119 155
Apery recurrence equation      101 146 155
Askey — Gasper identity      107
Askey — Gasper inequality      108
Askey — Wilson scheme      56
Associated Legendre functions      180
assume      8
Axiom      VI
Backward antidifference      62
Bailey identity      84 131
Bailey transformation      123
Bailey's hypergeometric database      84
Balanced hypergeometric series      43
Basic hypergeometric function      25
Bateman functions      179 205 211
Bateman integral representation      202
Bateman polynomials      59
Bessel differential equation      170 180
Bessel functions      2 121 170 180 205
Bessel polynomials      181
beta function      6 199
Bieberbach conjecture      29 108 179
Bieberbach conjecture, Weinstein proof      108
Big q-Legendre polynomials      56 122
Bilateral sum      13
Binomial sum identity      12
Binomial theorem      26 71 88
Binomial theorem, q-analogue      26 92 122
binomial(n,k)      7
Cauchy integral formula      207
Certificate, rational, of Almkvist — Zeilberger algorithm      195
Certificate, rational, of continuous Gosper algorithm      193
Certificate, rational, of extended Gosper algorithm      138
Certificate, rational, of extended WZ method      129
Certificate, rational, of hypergeometric term      72
Certificate, rational, of q-WZ method      90
Certificate, rational, of WZ method      85
Certificate, rational, of Zeilberger algorithm      103
Charlier polynomials      115
checksum(F,R,k,n)      90
Chu — Vandermonde identity      3 32 84
Classical discrete orthogonal polynomials      115
Classical orthogonal polynomials      181
Clausen formula      106
Clausen identity      91
Clausen product identity      106 118
Closedform(F,k,n)      106
Companion identity      89
Compatible recurrence equations      162
complexity      52 118 157 160 161
Confluence process      25 30
Constant term of Laurent polynomial      213
contdegreebound(p,q,x,x)      188
contdispersionset(q,r,x)      187
contfindf(p,q,r,x)      188
contgosper(f,x)      189
Continuous Gosper algorithm      183
Continuous q-Legendre polynomials      56 122
Contour integration      207
contratio(f,x)      187
contupdate(p,q,r,x)      188
CONVERT      7
Cosine function, q-analogue      177
Creative symmetrizing      162
Critical point of hyperexponential term      165
CTdiffeq(F,z,s(x))      213
CTrecursion(F,z,s(n))      213
Database of antiderivatives      61
Database of hypergeometric identities      31 84
Database of q-hypergeometric identities      40
de Branges' theorem      29 108 179
Decision procedure      52
Definite integration      183 194
Definite summation      12 80 93
Definite summation, natural bounds      13 23
Definite summation, non-natural bounds      23 104
degree(p,k)      67
degreebound(p,q,r,k)      76
Derangement numbers      159
Derivative rule      173 204
Derivative rule, Bateman functions      179
Derivative rule, Bessel functions      180
Derivative rule, Bessel polynomials      181
Derivative rule, Hermite polynomials      180
Derivative rule, hypergeometric function      27
Derivative rule, Laguerre polynomials      180
Derivative rule, Legendre polynomials      174 178
diff(f,x)      108
Difference operator      75
Differential equation, Abramowitz functions      203
Differential equation, Airy functions      205
Differential equation, Bateman functions      179
Differential equation, Bessel functions      170 180
Differential equation, Bessel polynomials      181
Differential equation, generalized Laguerre polynomials      209
Differential equation, Hermite polynomials      181
Differential equation, holonomic      2 164
Differential equation, hypergeometric      26
Differential equation, inhomogeneous      171 195
Differential equation, Jacobi polynomials      181
Differential equation, Laguerre polynomials      181
Differential equation, Legendre polynomials      2 168 209
Differential operator      199
Discrete orthogonal polynomials      115
Dispersion of polynomials      64
dispersionset(q,r,k)      66
Dixon identity      18 32 84
Dixon identity, q-analogue      92 122
Double sum identity      106
Dougall identity      84 98
Dougall identity, q-analogue      92 122
DSOLVE      206
Dual identity      89
Dummy variables in Maple      38
Duplication formula of $\Gamma$ function      16
Equivalent recurrence equations      162
Error function      187 193
Euler integral representation      201
Euler transformation      42 171
expand      7 14 29 110
Exponential function, q-analogue      177
Exponential generating function      210
Exponential generating function, Hermite polynomials      211
Exponential generating function, Legendre polynomials      213
Extended WZ certificate      129
extended_gosper algorithm      125
extended_gosper(a,k)      126
extended_gosper(a,k,m)      126 138
extended_sumrecursion      138
Factor      65 78
Factorial part      53 62 110
factorial(k)      7
Factorization, noncommutative      144 152
Factorization, rational      21 64 157
Falling factorial      75
Fasenmyer algorithm      47
Fasenmyer polynomials      58
fasenmyer(f,k,s(n),nmax)      51
Favard's theorem      59
Fibonacci numbers      57 118 212
findf(p,q,r,k)      76
find_mfold      138
Finite support      12 80 93 129
Fixed-point free permutations      159
Floor function      28
for loop in Maple      38
Forward antidifference      61
Forward difference operator      75
FPS package      180
frontend      187
Gamma function      4 196
Gamma function, duplication formula      16
Gamma function, reflection formula      6
GAMMA(z)      7
Gauss hypergeometric function      14 30
Gauss hypergeometric function, Bateman integral representation      202
Gauss hypergeometric function, Euler integral representation      201
Gauss identity      31 84 131
GCD      62
Gegenbauer polynomials      179
Gegenbauer polynomials, generating function      212
Generalized hypergeometric function      12
Generalized Laguerre polynomials      56 58 179 180 213
Generalized Laguerre polynomials, generating function      211
Generalized Laguerre polynomials, parameter derivative      120
Generalized Laguerre polynomials, Rodrigues formula      209
generateproducts(f)      153
Generating function      210
Generating function, exponential      210
Generating function, Gegenbauer polynomials      212
Generating function, generalized Laguerre polynomials      211
Generating function, Legendre polynomials      2 212
Generation of identities      99
Generation of identity      99
Gessel — Stanton identities      128
GFdiffeqCF,a,z,n,e(x))      210
GFrecursion(F,a,z,s(n))      210
GFUN package      VII
Gosper algorithm      61
Gosper algorithm, continuous version      183
Gosper algorithm, q-analogue      75
gosper(a,k)      76 88
Gosper-summable      62
Greatest common divisor      62
Greatest factorial factorization      74
Groebner basis      145
Hahn polynomials      115
Harmonic numbers      70 161
Hermite polynomials      59
Hermite polynomials, derivative rule      180
Hermite polynomials, differential equation      181
Hermite polynomials, exponential generating function      211
Hermite polynomials, Rodrigues formula      211
Holonomic differential equation      2 164
Holonomic operator      111
Holonomic recurrence equation      2 46
hsum package      VII 38 105 126 214
hsum.mpl      VII 214
Hyperexponential term      164 183
Hyperexponential term, antiderivative      183
Hyperexponential term, strictly      165
hypergeom(upper,lower,x)      36
Hypergeometric database      31
Hypergeometric database, Bailey      84
Hypergeometric differential equation      26
Hypergeometric function, basic      25
Hypergeometric function, confluent      14 30 203
Hypergeometric function, derivative rule      27
Hypergeometric function, Gauss      14 30 201 202
Hypergeometric function, generalized      12
Hypergeometric function, Kummer      14 30 203
Hypergeometric function, recurrence equation      27
Hypergeometric identity      12
Hypergeometric series      12
Hypergeometric series, balanced      43
Hypergeometric series, basic      25
Hypergeometric series, generalized      12
Hypergeometric series, k-balanced      43
Hypergeometric series, lower parameters      13
Hypergeometric series, nearly-poised      43
Hypergeometric series, Saalschuetzian      43
Hypergeometric series, upper parameters      13
Hypergeometric series, well-poised      43
Hypergeometric sum      12
Hypergeometric term      12
Hypergeometric term with respect to two variables      80
Hypergeometric term, (m,l)-fold      129
Hypergeometric term, admissible      137
Hypergeometric term, antidifference      61
Hypergeometric term, m-fold      124
Hypergeometric term, proper      53 110
Hypergeometric term, rational certificate      72
Hypergeometric transformation      3 39 171
Hypergeometric transformation, q-analogue      122
hyperrecursion(upper,lower,x,s(n))      137
hyperterm(upper,lower,x,k)      24 29 37
Identity, Andrews      127
Identity, Askey — Gasper      107
Identity, Bailey      84 131
Identity, binomial sum      12
Identity, Chu — Vandermonde      3 32 84
Identity, Clausen      91
Identity, Dixon      18 32 84
Identity, double sum      106
Identity, Dougall      84 98
Identity, Gauss      31 84 131 204
Identity, generation of      99 103
Identity, Gessel — Stanton      128
Identity, hypergeometric      12
Identity, integral sum      203
Identity, Jackson      92 122
Identity, Kummer      32 84 181
Identity, Pfaff — Saalschuetz      32 84
Identity, proving      82 99 127 173 203
Identity, q-Chu — Vandermonde      43 60 90 91 113 122 158
Identity, q-Dixon      92 122
Identity, q-Dougall      92 122
Identity, q-Gauss      40 43
Identity, q-Kummer      92 122
Identity, q-Pfaff — Saalschutz      40 60 92 113 122
Identity, Stanley      41
Identity, Strehl      55
Identity, Szekely      35
Identity, Watson      32 84 131
Identity, Whipple      32 84 131
Indefinite integration      183
Indefinite summation      61
Inequality of Askey and Gasper      108
infolevel      VI 73
Inhomogeneous differential equation      171 195
Inhomogeneous recurrence equation      105 195
int(f,x)      108 190
int(f,x=a..b)      8
intdiffrule(F,t,S(n,x))      204
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