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Wimp J. — Computation with recurrence relations
Wimp J. — Computation with recurrence relations



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Название: Computation with recurrence relations

Автор: Wimp J.

Язык: en

Рубрика: Математика/Численные методы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 310

Добавлена в каталог: 01.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $_{3}F_{2}(1)$, analyticity of      154
Hypergeometric function $_{3}F_{2}(1)$, Birkhoff series for      153
Hypergeometric function $_{3}F_{2}(1)$, coefficients in Jacobi series      158
Hypergeometric function $_{3}F_{2}(1)$, computation of      152
Hypergeometric function $_{3}F_{2}(1)$, minimal recursion for      159
Hypergeometric function $_{3}F_{2}(1)$, recursion relation for      153 158
Hypergeometric function $_{3}F_{2}(1)$, 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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