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A certain class of generating functions involving bilateral series

Published online by Cambridge University Press:  17 February 2009

H. M. Srivastava ,
M. A. Pathan  and
M. G. Bin-Saad
H. M. Srivastava
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada; e-mail: harimsri@math.uvic.ca.
M. A. Pathan
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, Uttar Pradesh, India; e-mail: mapathan@postmark.net and mmrOll@amu.up.nic.in.
M. G. Bin-Saad
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, Uttar Pradesh, India; e-mail: mapathan@postmark.net and mmrOll@amu.up.nic.in.
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Abstract

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The authors derive a general theorem on partly bilateral and partly unilateral generating functions involving multiple series with essentially arbitrary coefficients. By appropriately specialising these coefficients, a number of (known or new) results are shown to follow as applications of the theorem.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 3 , January 2003 , pp. 475 - 483
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Exton, H., “A note on some elementary generating functions of certain types of Lauricella polynomials”, Jñãnãbha Sect. A 3 (1973) 23–25.Google Scholar
[2]Exton, H., “A new generating function for the associated Laguerre polynomials and resulting expansions”, Jñãnãbha 13 (1983) 147–149.Google Scholar
[3]Goyal, S. P. and Laddha, R. K., “On the generalized Riemann zeta functions and the generalized Lambert transform”, Ganita Sandesh 11 (1997) 99–108.Google Scholar
[4]Gupta, K. C., Goyal, S. P. and Mukherjee, R., “Some results on generalized Voigt functions”, ANZIAM J. 44 (2002) 299–303.Google Scholar
[5]Hài, N. T., Marichev, O. I. and Srivastava, H. M., “A note on the convergence of certain families of multiple hypergeometric series”, J. Math. Anal. Appl. 164 (1992) 104–115.CrossRefGoogle Scholar
[6]Hubbell, J. H. and Srivastava, H. M., “Certain theorems on bilateral generating functions involving Hermite, Laguerre, and Gegenbauer polynomials”, J. Math. Anal. Appl. 152 (1990) 343–353.CrossRefGoogle Scholar
[7]Kamarujjama, M., Hussain, M. A. and Aftab, F., “On partly bilateral and partly unilateral generating relations”, Soochow J. Math. 23 (1997) 359–363.Google Scholar
[8]Pathan, M. A. and Yasmeen, , “On partly bilateral and partly unilateral generating functions”, J. Austral. Math. Soc. Ser. B 28 (1986) 240–245.Google Scholar
[9]Pathan, M. A. and Yasmeen, , “A note on a new generating relation for a generalized hypergeometric function”, J. Math. Phys. Sci. 22 (1988) 1–9.Google Scholar
[10]Srivastava, H. M. and Daoust, M. C., “Certain generalized Neumann expansions associated with the Kampé de Fériet function”, Nederl. Akad. Wetensch. Proc. Ser. A 72 = Indag. Math. 31 (1969) 449–457.Google Scholar
[11]Srivastava, H. M. and Daoust, M. C., “A note on the convergence of Kampé de Fériet's double hypergeometric series”, Math. Nachr. 53 (1972) 151–159.CrossRefGoogle Scholar
[12]Srivastava, H. M. and Karlsson, P. W., Multiple Gaussian hypergeometric series, Ellis Horwood Series: Mathematics and its Applications (Ellis Horwood Ltd., Chichester, 1985).Google Scholar
[13]Srivastava, H. M. and Manocha, H. L., A treatise on generating functions, Ellis Horwood Series: Mathematics and its Applications (Ellis Horwood Ltd., Chichester, 1984).Google Scholar
[14]Srivastava, H. M., Pathan, M. A. and Kamarujjama, M., “Some unified presentations of the generalized Voigt functions”, Comm. Appl. Anal. 2 (1998) 49–64.Google Scholar
[15]Szegö, G., Orthogonal polynomials, Amer. Math. Soc. Colloquium Publ. 23, fourth ed. (Amer. Math. Soc., Providence, RI, 1975).Google Scholar