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Certain theorems on bilinear and bilateral generating functions

Published online by Cambridge University Press:  17 February 2009

H. M. Srivastava  and
Yeong-Nan Yeh
H. M. Srivastava
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada; e-mail: [email protected].
Yeong-Nan Yeh
Affiliation:
Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan, Republic of China; e-mail: [email protected].
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Abstract

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It is observed (among other things) that a theorem on bilinear and bilateral generating functions, which was given recently in the predecessor of this Journal, does not hold true as stated and proved earlier. Several possible remedies and generalizations, which indeed are relevant to the present investigation of various other results on bilinear and bilateral generating functions, are also considered.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 4 , April 2002 , pp. 567 - 574
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Appell, P., “Sur les séries hypergéométriques de deux variables, et sur des équations différentielles linéaires aux dérivées partielles”, C. R. Acad. Sci. Paris 90 (1880) 296–298.Google Scholar
[2]Chen, M.-P. and Srivastava, H. M., “Some families of bilinear and bilateral generating functions”, Comput. Math. Appl. 28 (9) (1994) 1–7.CrossRefGoogle Scholar
[3]Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G., Higher transcendental functions, Vol. 1 (McGraw-Hill, New York, 1953).Google Scholar
[4]Lauricella, G., “Sulle funzioni ipergeometriche a più variabili”, Rend. Circ. Mat. Palermo 7 (1893) 111–158.CrossRefGoogle Scholar
[5]Mathur, B. L., “On some results involving Lauricella functions”, Bull. Calcutta Math. Soc. 70 (1978) 221–227.Google Scholar
[6]Mohammad, Ch. W., “Bilinear and bilateral generating functions of generalized polynomials”, J. Austral. Math. Soc. Ser. B 39 (1997) 257–270.CrossRefGoogle Scholar
[7]Saran, S., “Theorems on bilinear generating functions”, Indian J. Pure Appl. Math. 3 (1972) 12–20.Google Scholar
[8]Srivastava, H. M., “Orthogonality relations and generating functions for the generalized Bessel polynomials”, Appl. Math. Comput. 61 (1994) 99–134.Google Scholar
[9]Srivastava, H. M. and Gupta, L. C., “Some families of generating functions for the Jacobi polynomials”, Comput. Math. Appl. 29 (4) (1995) 29–35.CrossRefGoogle Scholar
[10]Srivastava, H. M. and Karlsson, P. W., Multiple Gaussian hypergeometric series (Ellis Horwood Ltd., Chichester, 1985).Google Scholar
[11]Srivastava, H. M. and Manocha, H. L., A treatise on generating functions (Ellis Horwood Ltd., Chichester, 1984).Google Scholar
[12]Whittaker, E. T. and Watson, G. N., A course of modern analysis: An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions, Reprint of the fourth (1927) edition (Cambridge University Press, Cambridge, 1996).CrossRefGoogle Scholar