Rogers–Dougall very well-poised sum
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1: 16.4 Argument Unity
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►It is very well-poised if it is well-poised and .
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Dixon’s Well-Poised Sum
… ►Rogers–Dougall Very Well-Poised Sum
… ►Dougall’s Very Well-Poised Sum
…2: 17.4 Basic Hypergeometric Functions
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►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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►The series (17.4.1) is said to be well-poised when and
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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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3: 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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4: Bibliography M
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A -analog of the summation theorem for hypergeometric series well-poised in
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Adv. in Math. 57 (1), pp. 14–33.
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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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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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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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5: 17.18 Methods of Computation
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►Method (2) is very powerful when applicable (Andrews (1976, Chapter 5)); however, it is applicable only rarely.
Lehner (1941) uses Method (2) in connection with the Rogers–Ramanujan identities.
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6: 17.12 Bailey Pairs
7: 17.14 Constant Term Identities
8: David M. Bressoud
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►His books are Analytic and Combinatorial
Generalizations of the Rogers-Ramanujan Identities, published in Memoirs of the American Mathematical Society 24, No.
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9: 26.10 Integer Partitions: Other Restrictions
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►where the last right-hand side is the sum over of the generating functions for partitions into distinct parts with largest part equal to .
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►where the inner sum is the sum of all positive odd divisors of .
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►where the inner sum is the sum of all positive divisors of that are in .
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