Bailey–Daum q-Kummer sum
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11—20 of 377 matching pages
11: 16.4 Argument Unity
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►Methods of deriving such identities are given by Bailey (1964), Rainville (1960), Raynal (1979), and Wilson (1978).
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►See Bailey (1964, pp. 19–22).
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►See Raynal (1979), Wilson (1978), and Bailey (1964).
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►See Bailey (1964, §4.4(4)).
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►See Bailey (1964, §§4.3(7) and 7.6(1)) for the transformation formulas and Wilson (1978) for contiguous relations.
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12: Bibliography
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A trinomial analogue of Bailey’s lemma and superconformal invariance.
Comm. Math. Phys. 192 (2), pp. 245–260.
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Umbral calculus, Bailey chains, and pentagonal number theorems.
J. Combin. Theory Ser. A 91 (1-2), pp. 464–475.
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Bailey’s Transform, Lemma, Chains and Tree.
In Special Functions 2000: Current Perspective and Future
Directions (Tempe, AZ), J. Bustoz, M. E. H. Ismail, and S. K. Suslov (Eds.),
NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 1–22.
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Theorems on generalized Dedekind sums.
Pacific J. Math. 2 (1), pp. 1–9.
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Bernoulli’s power-sum formulas revisited.
Math. Gaz. 90 (518), pp. 276–279.
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13: 5.24 Software
14: 17.9 Further Transformations of Functions
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Bailey’s Transformation of Very-Well-Poised
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17.9.19
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17.9.20
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15: Bibliography W
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A note on the trinomial analogue of Bailey’s lemma.
J. Combin. Theory Ser. A 81 (1), pp. 114–118.
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Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations.
Computers in Physics 10 (5), pp. 496–503.
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16: 16.6 Transformations of Variable
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16.6.1
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16.6.2
►For Kummer-type transformations of functions see Miller (2003) and Paris (2005a), and for further transformations see Erdélyi et al. (1953a, §4.5), Miller and Paris (2011), Choi and Rathie (2013) and Wang and Rathie (2013).
17: 17.4 Basic Hypergeometric Functions
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►It is slightly at variance with the notation in Bailey (1964) and Slater (1966).
In these references the factor is not included in the sum.
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17.4.3
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17.4.5
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17.4.7
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18: 18.18 Sums
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§18.18(vi) Bateman-Type Sums
►Jacobi
… ►For the Poisson kernel of Jacobi polynomials (the Bailey formula) see Bailey (1938). ►§18.18(viii) Other Sums
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Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions.
Ramanujan J. 6 (1), pp. 7–149.
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The and
Bailey transform and lemma.
Bull. Amer. Math. Soc. (N.S.) 26 (2), pp. 258–263.
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New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function.
Proc. Nat. Acad. Sci. U.S.A. 93 (26), pp. 15004–15008.
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Nested sums, expansion of transcendental functions, and multiscale multiloop integrals.
J. Math. Phys. 43 (6), pp. 3363–3386.
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On the representation of numbers as a sum of squares.
Quarterly Journal of Math. 48, pp. 93–104.
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