Bailey transformation of very-well-poised 8ϕ7
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1: 1.14 Integral Transforms
§1.14 Integral Transforms
►§1.14(i) Fourier Transform
… ►§1.14(iii) Laplace Transform
… ►Fourier Transform
… ►Laplace Transform
…2: 16.4 Argument Unity
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Rogers–Dougall Very Well-Poised Sum
… ►Dougall’s Very Well-Poised Sum
… ►Transformations for both balanced and very well-poised are included in Bailey (1964, pp. 56–63). A similar theory is available for very well-poised ’s which are 2-balanced. …3: 17.9 Further Transformations of Functions
§17.9 Further Transformations of Functions
… ►F. H. Jackson’s Transformations
… ►Bailey’s Transformation of Very-Well-Poised
… ►Sears–Carlitz Transformation
… ►Mixed-Base Heine-Type Transformations
…4: 17.4 Basic Hypergeometric Functions
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►It is slightly at variance with the notation in Bailey (1964) and Slater (1966).
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►The series (17.4.1) is said to be very-well-poised when , (17.4.11) is satisfied, and
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5: 17.12 Bailey Pairs
§17.12 Bailey Pairs
►Bailey Transform
… ►Bailey Pairs
… ►Weak Bailey Lemma
… ►Strong Bailey Lemma
…6: 16.6 Transformations of Variable
§16.6 Transformations of Variable
►Quadratic
… ►Cubic
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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).
7: 17.10 Transformations of Functions
§17.10 Transformations of Functions
►Bailey’s Transformations
… ►Other Transformations
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17.10.3
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17.10.5
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8: 17 q-Hypergeometric and Related Functions
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9: Bibliography B
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A Fortran-90 based multiprecision system.
ACM Trans. Math. Software 21 (4), pp. 379–387.
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Products of generalized hypergeometric series.
Proc. London Math. Soc. (2) 28 (2), pp. 242–254.
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Transformations of generalized hypergeometric series.
Proc. London Math. Soc. (2) 29 (2), pp. 495–502.
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The generating function of Jacobi polynomials.
J. London Math. Soc. 13, pp. 8–12.
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Generalized Hypergeometric Series.
Stechert-Hafner, Inc., New York.
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10: Bibliography W
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Extension of a quadratic transformation due to Whipple with an application.
Adv. Difference Equ., pp. 2013:157, 8.
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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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The cubic transformation of the hypergeometric function.
Quart. J. Pure and Applied Math. 41, pp. 70–79.
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Some transformations of generalized hypergeometric series.
Proc. London Math. Soc. (2) 26 (2), pp. 257–272.
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The Airy transform.
Amer. Math. Monthly 86 (4), pp. 271–277.
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