×

Some families of hypergeometric transformations and generating relations. (English) Zbl 1042.33005

Summary: By applying a quadratic transformation for the Gauss hypergeometric function, the authors derive a family of generating relations for a general polynomial system. Several interesting consequences of the main result, involving various classes of hypergeometric polynomials, are considered. Further generating relations associated with the Laguerre functions and polynomials are also investigated.

MSC:

33C20 Generalized hypergeometric series, \({}_pF_q\)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Erdélyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, F. G., (Higher Transcendental Functions, Volume I (1953), McGraw-Hill: McGraw-Hill New York) · Zbl 0051.30303
[2] Srivastava, H. M.; Manocha, H. L., A Treatise on Generating Functions (1984), Halsted Press, (Ellis Horwood, Chichester), John Wiley and Sons, New York · Zbl 0535.33001
[3] Prudnikov, A. P.; Bryčkov, Y. A.; Maričev, O. I., (Integrals and Series. Integrals and Series, Special Functions, Volume 2 (1988), Nauka: Nauka New York), (Translated from the Russian by N.M. Queen)
[4] Exton, H., A new hypergeometric generating relation, J. Indian Acad. Math., 21, 53-57 (1999) · Zbl 0933.33008
[5] Malani, S.; Rathie, A. K.; Choi, J., Another new hypergeometric generating relation contiguous to that of Exton, Comm. Korean Math. Soc., 15, 691-696 (2000) · Zbl 0988.33006
[6] Rainville, E. D., Special Functions (1960), Macmillan: Macmillan New York · Zbl 0050.07401
[7] Tempest, R. K.; Rosenhead, L., (Notes on the linearised equation for the velocity potential of the steady supersonic flow of a compressible fluid. Notes on the linearised equation for the velocity potential of the steady supersonic flow of a compressible fluid, Proc. London Math. Soc. Ser. 2 (1950)), 197-212, 51 · Zbl 0033.03302
[8] Bailey, W. N., (A note on the paper by Tempest and Rosenhead. A note on the paper by Tempest and Rosenhead, Proc. London Math. Soc. Ser. 2 (1950)), 213-214, 51 · Zbl 0033.03303
[9] Srivastava, H. M., A contour integral involving Fox’s \(H\)-function, Indian J. Math., 14, 1-6 (1972) · Zbl 0226.33016
[10] González, B.; Matera, J.; Srivastava, H. M., Some \(q\)-generating functions and associated generalized bypergeometric polynomials, Math. Comput. Modelling, 34, 1/2, 133-175 (2001) · Zbl 0991.33010
[11] Szegö, G., (Orthogonal Polynomials. Orthogonal Polynomials, American Mathematical Society Colloquium, Volume 23 (1975), American Mathematical Society: American Mathematical Society Providence, RI) · Zbl 0305.42011
[12] Brafman, F., Some generating functions for Laguerre and Hermite polynomials, Canad. J. Math., 9, 180-187 (1957) · Zbl 0078.25702
[13] Buchholz, H., The Confluent Hypergeometric Function with Special Emphasis on Its Applications, Volume 15, Springer Tracts in Natural Philosophy (1969), Springer-Verlag: Springer-Verlag New York, (Translated from the German by H Lichtblau and K. Wetzel) · Zbl 0169.08501
[14] Miller, W., (Lie Theory and Special Functions, Mathematics in Science and Engineering, Volume 43 (1968), Academic: Academic New York) · Zbl 0174.10502
[15] Exton, H., Series of Laguerre polynomials with respect to both order and degree, J. Indian Acad. Math., 15, 155-166 (1993) · Zbl 0831.33002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.