generalized%20hypergeometric%20series
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11—14 of 14 matching pages
11: Bibliography S
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Asymptotic series of generalized Lambert function.
ACM Commun. Comput. Algebra 47 (3), pp. 75–83.
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Generalized Hypergeometric Functions.
Cambridge University Press, Cambridge.
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On the logarithmic solutions of the generalized hypergeometric equation when
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Bull. Amer. Math. Soc. 45 (8), pp. 629–636.
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Computation of angular momentum coefficients using sets of generalized hypergeometric functions.
Comput. Phys. Comm. 22 (2-3), pp. 297–302.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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12: 20.11 Generalizations and Analogs
§20.11 Generalizations and Analogs
… ►§20.11(ii) Ramanujan’s Theta Function and -Series
… ►In the case identities for theta functions become identities in the complex variable , with , that involve rational functions, power series, and continued fractions; see Adiga et al. (1985), McKean and Moll (1999, pp. 156–158), and Andrews et al. (1988, §10.7). … ►As in §20.11(ii), the modulus of elliptic integrals (§19.2(ii)), Jacobian elliptic functions (§22.2), and Weierstrass elliptic functions (§23.6(ii)) can be expanded in -series via (20.9.1). … ►For applications to rapidly convergent expansions for see Chudnovsky and Chudnovsky (1988), and for applications in the construction of elliptic-hypergeometric series see Rosengren (2004). …13: Bibliography M
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A class of generalized hypergeometric summations.
J. Comput. Appl. Math. 87 (1), pp. 79–85.
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A new symmetry related to for classical basic hypergeometric series.
Adv. in Math. 57 (1), pp. 71–90.
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A -analog of hypergeometric series well-poised in and invariant -functions.
Adv. in Math. 58 (1), pp. 1–60.
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A -analog of the Gauss summation theorem for hypergeometric series in
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Adv. in Math. 72 (1), pp. 59–131.
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A -analog of a Whipple’s transformation for hypergeometric series in
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Adv. Math. 108 (1), pp. 1–76.
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14: Bibliography G
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Contiguous relations and summation and transformation formulae for basic hypergeometric series.
J. Difference Equ. Appl. 19 (12), pp. 2029–2042.
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Basic Hypergeometric Series.
Encyclopedia of Mathematics and its Applications, Vol. 35, Cambridge University Press, Cambridge.
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Basic Hypergeometric Series.
Second edition, Encyclopedia of Mathematics and its Applications, Vol. 96, Cambridge University Press, Cambridge.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Multilateral summation theorems for ordinary and basic hypergeometric series in
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SIAM J. Math. Anal. 18 (6), pp. 1576–1596.
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