generalized hypergeometric series
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11: 18.5 Explicit Representations
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§18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions
…12: 16.25 Methods of Computation
§16.25 Methods of Computation
►Methods for computing the functions of the present chapter include power series, asymptotic expansions, integral representations, differential equations, and recurrence relations. They are similar to those described for confluent hypergeometric functions, and hypergeometric functions in §§13.29 and 15.19. …13: 13.12 Products
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13.12.1
►For generalizations of this quadratic relation see Majima et al. (2000).
►For integral representations, integrals, and series containing products of and see Erdélyi et al. (1953a, §6.15.3).
14: Howard S. Cohl
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►Cohl has published papers in orthogonal polynomials and special functions, and is particularly interested in fundamental solutions of linear partial differential equations on Riemannian manifolds, associated Legendre functions, generalized and basic hypergeometric functions, eigenfunction expansions of fundamental solutions in separable coordinate systems for linear partial differential equations, orthogonal polynomial generating function and generalized expansions, and -series.
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15: 16.5 Integral Representations and Integrals
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►In this event, the formal power-series expansion of the left-hand side (obtained from (16.2.1)) is the asymptotic expansion of the right-hand side as in the sector , where is an arbitrary small positive constant.
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16: Bibliography V
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On the series expansion method for computing incomplete elliptic integrals of the first and second kinds.
Math. Comp. 23 (105), pp. 61–69.
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An infinite series of Weber’s parabolic cylinder functions.
Proc. Benares Math. Soc. (N.S.) 3, pp. 37.
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A note on the asymptotic expansion of generalized hypergeometric functions.
Anal. Appl. (Singap.) 12 (1), pp. 107–115.
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Fourier series representation of Ferrers function
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Asymptotic expansion of the generalized hypergeometric function as for
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Anal. Appl. (Singap.) 21 (2), pp. 535–545.
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17: 34.13 Methods of Computation
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►Methods of computation for and symbols include recursion relations, see Schulten and Gordon (1975a), Luscombe and Luban (1998), and Edmonds (1974, pp. 42–45, 48–51, 97–99); summation of single-sum expressions for these symbols, see Varshalovich et al. (1988, §§8.2.6, 9.2.1) and Fang and Shriner (1992); evaluation of the generalized hypergeometric functions of unit argument that represent these symbols, see Srinivasa Rao and Venkatesh (1978) and Srinivasa Rao (1981).
►For symbols, methods include evaluation of the single-sum series (34.6.2), see Fang and Shriner (1992); evaluation of triple-sum series, see Varshalovich et al. (1988, §10.2.1) and Srinivasa Rao et al. (1989).
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18: Bibliography K
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On the zeros of some generalized hypergeometric functions.
J. Math. Anal. Appl. 243 (2), pp. 249–260.
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Approximation Formulae for Generalized Hypergeometric Functions for Large Values of the Parameters.
J. B. Wolters, Groningen.
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Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators.
SIGMA Symmetry Integrability Geom. Methods Appl. 11, pp. Paper 074, 22.
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HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
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Some special cases of the generalized hypergeometric function
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J. Comput. Appl. Math. 78 (1), pp. 79–95.
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