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On partly bilateral and partly unilateral generating functions

  • M. A. Pathan and Yasmeen (a1)

Abstract

The purpose of this work is to begin the development of a theory of generating functions that will not only include the generating functions which are partly bilateral and partly unilateral but also provide a set of expansions, by taking successive partial derivatives with respect to one of the variables of the generating relations. Our starting point is a result of Exton [4] on associated Laguerre polynomials whose application gives certain generating functions of the polynomials of Jacobi and Appell, and functions of n variables of Lauricella.

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References

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[1]Bailey, W.N., Generated hypergeometric series, (Cambridge University Press, London, 1935).
[2]Erdélyi, A. et al. , Tables of integral transforms, Vol. 1 (McGraw-Hill Book Co. Inc., New York, 1954).
[3]Erdélyi, A. et al. , Higher transcendental functions, Vol. 1 (McGraw-Hill Book Co. Inc., New York, 1953).
[4]Exton, H., A new generating function for the associated Laguerre polynomials and resulting expansions, Jnānābha, 13 (1983), 147149.
[5]Exton, H., Multiple hypergeometric functions and applications, (Ellis Horwood Limited, Chichester, U.K., 1976).
[6]Rainville, E.D., Speical functions, (The Macmillan Co., New York, 1960).
[7]Schiff, L., Quantum mechanics, (McGraw-Hill, New York, 1955).
[8]Srivastave, H.M. and Manocha, H.L., A treatise on generation functions (Ellis Horwood Limited, Chichester, 1984).
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