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| Wimp J. — Computation with recurrence relations |
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| Предметный указатель |
Adjoint equation 267
Analytic solutions of functional equation 245
Aquifer function 101
Ascending Landen transformation 262
Associated Legendre function 73
Associated polynomials 53
Asymptotic behavior of sums 277
Attractor 219
Autonomous systems 211
Bessel function, computation of 79
Bessel function, error in computation 41
Bessel function, modified 30 67 133 185
Bessel function, modulus of 184
Bessel function, series of 168
Bessel function, spherical 287
Bessel function, zeros of 82
beta function 157
Bickley function 112
Bifurcation in trajectory 219
Birkhoff — Trjitzinsky theorem 274
Birkhoffset 274
Borchardt algorithm 237 241
Canonical set 274
Cardinal interpolation 16
Carlson 212 237
Casorati determinant 265
Cauchy equation 225
Characteristic equation 270
Charlier polynomials 181
Chebyshev expansions, evaluation of sums of 170
Chebyshev expansions, expanded in Chebyshev polynomials 175
Chebyshev expansions, explicit expression for 161
Chebyshev expansions, general properties of 161
Chebyshev expansions, obtained by interpolation 175
Chebyshev expansions, obtained from power series 174
Chebyshev expansions, series of 161
Chebyshev expansions, solutions of nonlinear d.e. 202
Christoffel numbers 56
Clenshaw algorithm, definition of 165
Clenshaw algorithm, error of 167
Clenshaw algorithm, generalized 189
Clenshaw averaging process 57 122
Composition of operators 196
Condition number 8 171
Confluent hypergeometric function, asymptotic formula for 276
Confluent hypergeometric function, computation of 61
Confluent hypergeometric function, expansions in such functions 185
Confluent hypergeometric function, integral of error function 20
Continued fraction 46
Contracting mapping 212
Convergence, degree of 210
Convergence, linear 210
Convergence, pth order 209
Convergence, quadratic 209 259
Conversion of polynomial expansions 172
Coulomb energy integrals 287
Descending Gauss transformation 260
Difference equation, adjoint equation for 267
Difference equation, asymptotic theory of linear 270
Difference equation, finite sums of solutions 165
Difference equation, fundamental set for 266
Difference equation, generalized linear 266
Difference equation, infinite order 128
Difference equation, rational coefficients 280
Difference equation, solution second order linear 269
Difference equation, written as system 5
Difference operator 196 265
Differential equation, adjoint equation for 179
Differential equation, series solutions of 177
Differential equation, Taylor series for 178
Divergent algorithms 219
Dominant solution 19
Duality theorem 31 113
Eigenvalues of Mathieu equation 82
Elliott algorithm 189
Elliptic function 248 263
Elliptic integral 184 215 217 243
Equation of invariant curves 229
Error function 125
Evaluation of finite sums 165
Exponential function, Chebyshev series for 125
Exponential function, computation of partial sums for 13
Exponential function, expanded in Legendre polynomials 195
Exponential integral 184 190
Exponential integral En(x) 15
Exponential integral, Chebyshev series for 127
Exponential sums 277
Fixed point 211 218
Formal linear independence 274
Formal power series 289
Formal series 54 180
Formal series solution 272
Formal series, construction of 273
Formal series, definition of 272
Formal series, equality of 273
Forward elimination 90
Functional equation 245 249
Fundamental set 266
G function 125
Gamma function, Chebyshev coefficients for 130
Gamma function, derivatives of 131
Gamma function, inequality for 155
Gatteschi 232
Gatteschi algorithm 245
Gauss algorithm, convergence of 219 230
Gauss algorithm, definition of 212
Gauss algorithm, properties of 240
Gaussian hypergeometric function, beta integral of 152
Gaussian hypergeometric function, computation of 70
Gaussian hypergeometric function, difference equation for 292
Gaussian hypergeometric function, Jacobi polynomial expansion of 158
Gaussian quadrature 55
Gaussian weights 56
Gegenbauer expansions, recurrences for coefficients of 186
Gegenbauer polynomials, general properties of 164
Gegenbauer polynomials, moments of 57
Gegenbauer polynomials, series of 165 186
Generalized continued fraction 51
Generalized hypergeometric function, computation of 109
Generalized hypergeometric function, difference equation for 291
| Generalized Miller algorithm 104
Henon attractor 220
Horn function 182
Hypergeometric function  , analyticity of 154
Hypergeometric function , Birkhoff series for 153
Hypergeometric function , coefficients in Jacobi series 158
Hypergeometric function , computation of 152
Hypergeometric function , minimal recursion for 159
Hypergeometric function , recursion relation for 153 158
Hypergeometric function , representation by gamma functions 160
Incomplete elliptic integrals 260
Incomplete gamma function 13 69 180 183
Indecomposable attractor 222
Index of stability 7
Inequality of generalized means 224
Infinite products 231
Integral invariant for algorithm 214
Interation sequence 210
Invariant curve 229
Invariant curve for algorithm 218
Invariant for algorithm 213 261
Invariant for system 211
Invariant surface for algorithm 217
Jacobi function 152
Jacobi matrix 55
Jacobi polynomials, beta integral of 164
Jacobi polynomials, general properties of 163
Jacobi polynomials, of imaginary argument 75
Jacobi polynomials, series of 163
Jacobi zeta function 260
Jensen equation 224
Kinetic energy integrals 287
Lagrange algorithm 212
Landen transformation 212
Laplace transform of Bessel function 135
Legendre expansions 195
Legendre function 73
Lemniscate constants 243
Lemniscate function 243
Lewanowicz algorithm 186
Linear dependence of sequences 265
Lipschitz condition 218
Lipschitz continuity 218
Logarithm function, infinite product for 228
Lommel function 200
Lozier 139
LU decomposition 96
Mathieu equation 82
Mean, arithmetic 213 224
Mean, exponential 224
Mean, generalized 223
Mean, generating function for 223
Mean, geometric 224
Mean, harmonic 213 224
Mean, homogeneous 223
Mean, inequalities for 224
Mean, logarithmeic 226
Mean, quasiarithmetic 223
Mean, root power 224
Mean, symmetric 223
Mean, weighted arithmetic 229
Method of averaging 95
Miller algorithm 24
Minimal recurrence 179
Minimal solution 19
Minimum operator 197
Mixed recurrences 188
Modified moments 57 87 202
Moment integral 28 107 131
Moment problem 53
Nesting procedure 165
Noerlund sum 265
Nonlinear differential equations 202
Nonlinear differential equations, Chebyshev series for 207
Nonperiodic trajectories 219
Normalizing series 29
Olver algorithm 86
Olver growth theorems 282
Operator rings 196
Orthogonal polynomials 53
Parabolic cylinder function 107
Periodic attractor 220
Permanence principle 289
Perron theorem 270
Perron — Kreuser theorem 281
Picard iteration 202
Pincherle 35
Pringsheim 36
QL algorithm 56
R function 237
Rearrangement of interpolating series 175
Rearrangement of polynomial expansions 172
Rearrangement of power series 174 175
Rectification of lemniscate 243
Recurrence of lowest order 202
Recurrence relation see "Difference equation"
Recursion relation see "Difference equation"
Repeated integrals of error function 20
Riemann zeta function 134
Root-proper 180
Schroeder equation 252
Scraton 37
Self-conjugate curve 229
Stability 8
Stieltjes moment integral 131
Strange attractors 219
Struve function 89 184
Sums of solutions of recurrences 165
Taylor series, converted into orthogonal series 172
Taylor series, rearrangement of 174
Taylor series, solutions of d.e. 178
Thacher algorithm 178
Theta function 237
Toroidal function 75
Trajectory of system 1 211
Tricomi algorithm 248
Trigonometric integrals, computation of 254
Trigonometric integrals, convergence of algorithm for 259
van der Pol equation 207
Weak stability 8
Weber function 89
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