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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 |
intdifieq(F,t,S(x)) 197
Integer-linear 12
Integral formula of Cauchy 207
Integral representation, Bateman 202
Integral representation, Bateman functions 205
Integral representation, Bessel functions 205
Integral representation, Beta function 6 199
Integral representation, Euler 201
Integral representation, Gamma function 4 196
Integral representation, generating function 210
Integral representation, Kummer hypergeometric function 203
Integral representation, Legendre polynomials 207
Integral representation, Rodrigues formula 207
Integral sum identity 203
Integration rule 175
Integration rule, Bessel polynomials 181
Integration rule, Jacobi polynomials 176 181
Integration rule, Legendre polynomials 176
Integration, contour 207
Integration, definite 183 194
Integration, indefinite 183
INTERFACE 215
intrecursion(F,t,S(n)) 197
isolve 64 78
Jackson identity 92 122
Jacobi polynomials 120 181
Jacobi polynomials, integration rule 176 181
Jacobi polynomials, parameter derivative 121
Jacobi polynomials, Rodrigues formula 212
k-balanced hypergeometric series 43
k-free recurrence equation 45
kfreereec(f,k,n,kmax,nmax) 49
Krawtchouk polynomials 115
Kummer hypergeometric function 14 30
Kummer hypergeometric function, integral representation 203
Kummer identity 32 84
Kummer identity, q-analogue 92 122
Kummer transformation 42 171
Laguerre polynomials 51
Laguerre polynomials, differential equation 181
Laguerre polynomials, generalized 56 58 179 180
Laguerre polynomials, generalized, derivative rule 180
Laguerre polynomials, generalized, generating function 211
Laguerre polynomials, generalized, parameter derivative 120
Laguerre polynomials, generalized, Rodrigues formula 209
Laguerre polynomials, q-analogue 56 122
Legendre functions, associated 180
Legendre polynomials 1 22 42 101 178
Legendre polynomials, derivative rule 174 178
Legendre polynomials, differential equation 2 168
Legendre polynomials, exponential generating function 213
Legendre polynomials, generating function 2 212
Legendre polynomials, integration rule 176
Legendre polynomials, q-analogues 60
Legendre polynomials, recurrence equation 2 46 57
Legendre polynomials, Rodrigues formula 1 207
Legendre polynomials, Schlaefli's integral 205 207
Little q-Legendre polynomials 55 122
Little q-Legendre polynomials, recurrence equation 60
Lower parameters of hypergeometric series 13
m-fold antidifference 124
m-fold hypergeometric term 124
Macsyma VI
MAP 49
Maple share library 24 180
Mathematica VII
Meixner polynomials 115
Mgfun package VII
Monic polynomial 141
Natural bounds of definite sum 13 23
Nearly-poised hypergeometric series 43
Non-natural bounds 104
Noncommutative factorization 144 152
normal 14 49 109 192
Number of derangements 159
Operator, differential 199
Operator, holonomic 111
Operator, shift 110
Option remember 139
Optional argument of a Maple procedure 49
Ordinary differential equation 164
Orthogonal polynomials, classical 181
Orthogonal polynomials, classical discrete 115
Parameter derivative, Jacobi polynomials 121
Parameter derivative, Laguerre polynomials 120
Pascal triangle 51
Petkovsek algorithm 140
Petkovsek algorithm, q-analogue 158
Pfaff transformation 39 171
Pfaff — Saalschuetz identity 32 84
Pochhammer symbol 5
pochhammer(a,k) 98
Polynomial part 53 62 110
Polynomial resultant 64 184 189
Polynomial solutions of recurrence equations 140
Polynomials, Bateman 59
Polynomials, Bessel 181
Polynomials, big q-Legendre 56 122
Polynomials, Charlier 115
Polynomials, continuous q-Legendre 56 122
Polynomials, discrete 115
Polynomials, Fasenmyer 58
Polynomials, Gegenbauer 179 212
Polynomials, Hahn 115
Polynomials, Hermite 59 180 181 211
Polynomials, Jacobi 120 176 181 212
Polynomials, Krawtchouk 115
Polynomials, Laguerre 51 56 58 120 179—181 209 211 213
Polynomials, Legendre 1 22 42 46 57 101 168 174 176 178 205 207
Polynomials, little q-Legendre 55 60 122
Polynomials, Meixner 115
Polynomials, monic 141
Polynomials, orthogonal 181
Polynomials, q-Laguerre 56 122
Polynomials, Wilson 116
Power series 13
primedispersion(q,r,k) 66
print 215
Probability integral 9
Proper hypergeometric term 53 110
Proving identities 82 99 127 173 203
q-analogue 26
q-binomial coefficient 26
q-binomial theorem 26 92 122
q-brackets 26
q-Chu — Vandermonde identity 43 60 90 91 113 122 158
q-cosine function 177
q-derivative operator 176
q-Dixon identity 92 122
q-Dougall identity 92 122
q-exponential function 177
q-factorial 26
q-gamma function 26
q-Gauss identity 40 43
q-Gosper algorithm 75
q-hypergeometric database 40
q-hypergeometric database function 25
q-hypergeometric database series 25
q-hypergeometric database term 25
q-hypergeometric database transformation 122
q-Kummer identity 92 122
q-Laguerre polynomials 56 122
| q-Legendre polynomials, big 56 122
q-Legendre polynomials, continuous 56 122
q-Legendre polynomials, little 55 60 122
q-Petkovsek algorithm 158
q-Pfaff — Saalschiitz identity 40 60 92 113 122
q-Pochhammer symbol 25
q-sine function 177
q-Vandermonde identity 60 90 91 113 122 158
q-WZ method 90
q-Zeilberger algorithm 113
qbinomial(n,k,q) 40
qbrackets(k,q) 40
qeum package VII 40 56 75 113 158 177 214
qfactorial(k,q) 40
qfasenmyer(term,q,k,S(n),kmax,nmax) 56
qGAMMA(k,q) 40
qgosper(texm,q,k) 75
qphihyperterm(upper,lower,q,x,k) 40
qpochhammer(a,q,k) 40
qratio(expr,k) 40
qrecsolve(rec,q,S(n)) 158
qsimpcomb(expr) 40
qsum.mpl VII 40 214
qsumdiifeq(F,q,k,S(x)) 177
qsumrecuxsion(F,q,k,S(n)) 113
Quadratic transformation 180
Quoting in Maple to release assignments 89
Quoting in Maple, dummy variables 96
qWZcertificate(F,k,n) 90
radnormal 192
ratio(a,k) 24 37
Rational certificate of Almkvist — Zeilberger algorithm 195
Rational certificate of continuous Gosper algorithm 193
Rational certificate of extended Gosper algorithm 138
Rational certificate of extended WZ method 129
Rational certificate of hypergeometric term 72
Rational certificate of q-WZ method 90
Rational certificate of WZ method 85
Rational certificate of Zeilberger algorithm 103
Rational factorization 21 64 157
Rational-linear arguments 12 134
rec2hyper(rec,s(n)) 154
rec2poly(rec,s(n)) 146
rechyper(rec,s(n)) 161
recpoly(rec,s(n)) 160
Recurrence equation of discrete orthogonal polynomials 115
Recurrence equation, Apery numbers 101 146 155
Recurrence equation, holonomic 2 46
Recurrence equation, hypergeometric function 27
Recurrence equation, inhomogeneous 105 195
Recurrence equation, k-free 45
Recurrence equation, Laguerre polynomials 52
Recurrence equation, Legendre polynomials 2 46 57
Recurrence equation, little q-Legendre polynomials 60
Reduce VII 145 200
Reflection formula of  function 6
remember option 139
Resultant of polynomials 64 184 189
resultant(q,r,k) 64
Risch algorithm 61 192
Risch — Bronstein algorithm 183 193
rodriguasrecursion(g,h,x,s(n)) 208
Rodrigues formula 207
Rodrigues formula, generalized Laguerre polynomials 209
Rodrigues formula, Hermite polynomials 211
Rodrigues formula, Jacobi polynomials 212
Rodrigues formula, Legendre polynomials 1 207
rodriguesdiffeq(g,h,n,e(n)) 208
Saalschuetz identity 32 84
Saalschuetzian hypergeometric series 43
Schlaefli's integral 205 207
seq(f,j=list) 38
share library in Maple 24 180
Shift operator 110
Shift structure 64
Shifted factorial 5
simpcomb algorithm 15
simpcomb(expr) 24
SIMPLIFY 7 14
simplify_gamma algorithm 15
simplify_power algorithm 15
Sine function, q-analogue 177
Solve 45
Stanley identity 41
Stanton conjecture 122
Stirling formula 77
Strehl identity 55
Strictly hyperexponential term 165
subs(a=b,c) 50
sum(a,k) 73
sum(a,k=m..n) 23 37
sum2qhyper(expr,q,k) 40
sumdeltanabla(F,k,s(x)) 116
sumdiffeq(F,k,S(x)) 168
sumdiffrule(F,k,S(n,x)) 174
sumintrule(F,k,S(n,x)) 175
Summable, Gosper- 62
Summation by parts 76
Summation, definite 12 80 93
Summation, definite, natural bounds 13 23
Summation, definite, non-natural bounds 23 104
Summation, indefinite 61
sumracursion(F,k,s(n)) 100 119 137
sumrecursion(F,k=a..b,s(n)) 105
Sumtohyper(f,k) 38
sumtools package 24 38 74 88 126 137
Support, finite 12 80
Symmetrizing 162
Szekely identity 35
theorem, Favard 59
time() 67
Transformation, Bailey 123
Transformation, Euler 42 171
Transformation, hypergeometric 171
Transformation, Kummer 42 171
Transformation, Pfaff 39 171
Transformation, q-analogue 122
Transformation, quadratic 180
Transformation, Watson 122
Transformation, Whipple 116 180
traperror 88
update(p,q,r,k) 76
Upper parameters of hypergeometric series 13
Vandermonde identity 3 32 84
verboseproc 215
Watson identity 32 84 131
Watson transformation 122
Weinstein proof of Bieberbach conjecture 108
Well-poised hypergeometric series 43
Whipple identity 32 84 131
Whipple transformation 116 180
Wilf — Zeilberger method 82
Wilson polynomials 116
WZ certificate 85
WZ certificate, extended 129
WZ certificate, q-analogue 90
WZ method 82
WZ method, q-analogue 90
WZcertificate(F,k,n) 88
WZcertificate(F,k,n,m,l) 132
Zeilberger algorithm 93 103
Zeilberger algorithm, q-analogue 113
zeilberger(F,k,e(n)) 96
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