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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the $q$-analogues of some transformations of nearly-poised hypergeometric series
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by B. Nassrallah and Mizan Rahman PDF
Trans. Amer. Math. Soc. 268 (1981), 211-229 Request permission

Abstract:

A number of transformation formulas for very well-poised basic hypergeometric series have been obtained which, in the limit $q \to 1 -$, approach the known transformation formulas for nearly-poised ordinary hypergeometric series.
References
  • R. P. Agarwal and Arun Verma, Generalized basic hypergeometric series with unconnected bases, Proc. Cambridge Philos. Soc. 63 (1967), 727–734. MR 212216, DOI 10.1017/s0305004100041724
  • George E. Andrews, Applications of basic hypergeometric functions, SIAM Rev. 16 (1974), 441–484. MR 352557, DOI 10.1137/1016081
  • George E. Andrews, Problems and prospects for basic hypergeometric functions, Theory and application of special functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975) Math. Res. Center, Univ. Wisconsin, Publ. No. 35, Academic Press, New York, 1975, pp. 191–224. MR 0399528
  • George E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. MR 0557013
  • Jacques Labelle, Tableau d’Askey, Orthogonal polynomials and applications (Bar-le-Duc, 1984) Lecture Notes in Math., vol. 1171, Springer, Berlin, 1985, pp. xxxvi–xxxvii (French). MR 838967
  • Richard Askey and James Wilson, A set of orthogonal polynomials that generalize the Racah coefficients or $6-j$ symbols, SIAM J. Math. Anal. 10 (1979), no. 5, 1008–1016. MR 541097, DOI 10.1137/0510092
  • R. Askey and M. E. H. Ismail, A generalization of ultraspherical polynomials, Technical summary report #1851, Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1978.
  • W. N. Bailey, Generalized hypergeometric series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 32, Stechert-Hafner, Inc., New York, 1964. MR 0185155
  • W. N. Bailey, A transformation of nearly-poised basic hypergeometric series, J. London Math. Soc. 22 (1947), 237–240 (1948). MR 23964, DOI 10.1112/jlms/s1-22.3.237
  • L. Carlitz, Some formulas of F. H. Jackson, Monatsh. Math. 73 (1969), 193–198. MR 248035, DOI 10.1007/BF01300534
  • Mizan Rahman, A nonnegative representation of the linearization coefficients of the product of Jacobi polynomials, Canadian J. Math. 33 (1981), no. 4, 915–928. MR 634149, DOI 10.4153/CJM-1981-072-9
  • —, The linearization of the product of continuous $q$-Jacobi polynomials, Canad. J. Math. (to appear).
  • Lucy Joan Slater, Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966. MR 0201688
  • Arun Verma, A quadratic transformation of a basic hypergeometric series, SIAM J. Math. Anal. 11 (1980), no. 3, 425–427. MR 572192, DOI 10.1137/0511039
  • F. J. W. Whipple, Some transformations of generalized hypergeometric series, Proc. London Math. Soc. (2) 26 (1927), 257-272.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 268 (1981), 211-229
  • MSC: Primary 33A30
  • DOI: https://doi.org/10.1090/S0002-9947-1981-0628455-0
  • MathSciNet review: 628455