Transformation and Summation Formulas for Kampé de Fériet SeriesF0:31:1(1,1)

Pitre, Sangita N.; Jeugt, J. Van der

doi:10.1006/jmaa.1996.0306

Cited by 20 publications

(7 citation statements)

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“…On June 6, 1994, the author sent Van der Jeugt a proof of (5.3) and the derivation of a q-analogue of Erdélyi's fractional integral (1.5) by using the q-binomial integral [7, (1.11.7)], the transformation formula [7,III.3], the q-Gauss sum [7,II.8] and changes in order of summation. This enabled Van der Jeugt, Pitre, and Srinivasa Rao to state formula (5.1) in [11, (40) with a change in parameters], and inspired them to use similar methods to derive the transformation and summation formulas contained in [11], [12], [13], also see [9]. It also started the author's work on the derivation of the formulas contained in this paper.…”

Section: Summation Formulas For Some Basic Kampé De Fériet Seriesmentioning

confidence: 99%

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𝑞-extensions of Erdélyi’s fractional integral representations for hypergeometric functions and some summation formulas for double 𝑞-Kampé de Fériet series

Gasper¹

2000

𝑞-Series From a Contemporary Perspective

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Dedicated to Dick Askey on the occasion of his 66th birthday, and to the memory of D.B. Sears whose 4 φ 3 transformation formula plays a crucial role in this paper Abstract. q-Analogues of Erdélyi's fractional integral representations of hypergeometric functions are derived and extended to expansion formulas for certain 3 φ 2 and 4 φ 3 basic hypergeometric series. Special cases of some of the derived formulas are used to derive new summation formulas for double hypergeometric and basic hypergeometric Kampé de Fériet series, including a summation formula for a double basic hypergeometric Kampé de Fériet series that was conjectured in work of J. Van der Jeugt, S.N. Pitre, and K. Srinivasa Rao on the evaluation of the 9-j recoupling coefficients appearing in the quantum theory of angular momentum.

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Section: Summation Formulas For Some Basic Kampé De Fériet Seriesmentioning

confidence: 99%

“…I would like to thank Joris Van der Jeugt for encouraging me to work on proving formulas (5.1) and (5.3), and for sending preprints of [9] and [11].…”

Section: Summation Formulas For Some Basic Kampé De Fériet Seriesmentioning

confidence: 99%

𝑞-extensions of Erdélyi’s fractional integral representations for hypergeometric functions and some summation formulas for double 𝑞-Kampé de Fériet series

Gasper¹

2000

𝑞-Series From a Contemporary Perspective

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“…3 it was also proved after tedious rearrangement of the fourfold sum 8 in frames of the usual angular momentum ͓SU͑2͒ representation theory͔ technique, by means of the Chu-Vandermonde summation formulas. Different computational, [9][10][11][12] polynomial, 13,14 rearrangement, [15][16][17][18][19][20] specification, 21,22 and other 23 aspects of this triple sum series were considered. Its analytical continuation was also adapted 24 for the isoscalar factors of the Clebsch-Gordan ͑CG͒ coefficients of the Lorentz or SL(2,C) group.…”

Section: Introductionmentioning

confidence: 99%

The triple sum formulas for 9j coefficients of SU(2) and uq(2)

Alisauskas

2000

Journal of Mathematical Physics

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Seven different triple sum formulas for 9 j coefficients of the quantum algebra u q (2) are derived, using for these purposes the usual expansion of q-9 j coefficients in terms of q-6 j coefficients and recently derived summation formula of twisted q-factorial series ͑resembling the very well-poised basic hypergeometric 5 4 series͒ as a q-generalization of Dougall's summation formula of the very well-poised hypergeometric 4 F 3 (Ϫ1) series. This way for qϭ1 Rosengren's second proof of the SU͑1,1͒ case is adapted for the SU͑2͒ case to derive the known triple sum formula of Ališauskas and Jucys, as well as six new independent triple sum formulas for the Wigner 9 j coefficients of the angular momentum theory. The mutual rearrangement possibilities of the derived triple sum formulas by means of the Chu-Vandermonde summation formulas are considered and applied to derive several versions of double sum formulas for the stretched q-9 j coefficients, which give new rearrangement and summation formulas of special Kampé de Fériet functions and their q-generalizations.

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“…When +r = 3 and + u = 2, the double Clausen hypergeometric series F :r ;s :u;v have been investigated extensively. In particular, many transformation and reduction formulae on F 122 022 and F 033 111 have been obtained by Sighal [4], Karlsson [5,6], Pitre and Van der Jeugt [7] and Van der Jeugt et al [8,9], where the last three papers have completed the study of double hypergeometric series arising from the framework of the so-called 9-j coefficients of angular momentum theory.…”

Section: Introductionmentioning

confidence: 98%