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| Авторизация |
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| Koepf W. — Hypergeometric summation. An algorithmic approach to summation and special function identities |
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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,r,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  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, rationed 21 64 157
Falling factorial 75
fasenmyar(f,k,s(n),nmax) 51
Fasenmyer algorithm 47
Fasenmyer polynomials 58
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
GFdiffeq(F,a,z,n,s(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
intdiffeq(F,t,S(x)) 197
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