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A note on certain bilinear and bilateral generating relations for the laguerre polynomial

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Abstract

The author presents here a systematic analysis of certain bilinear and bilateral generating relations associated with the generalized Laguerre polynomials {Ln (a) (x)} defined by

$$(1 - t)^{ - 1 - \alpha } \exp \left( { - \frac{{xt}}{{1 - t}}} \right) = \sum\limits_{n = 0}^\infty {L_n ^{(\alpha )} (x) t^n .} $$

It is observed that the four formulas proved recently by Jain [7] are only specialized or limiting forms of the results of Erdélyi,[4] Meixner [8] and the author [12–14].

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Authors and Affiliations

  1. Department of Mathematics, University of Victoria, Victoria, British Columbia, Canada

    H. M. Srivastava

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  1. H. M. Srivastava
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Communicated by Prof. P. L. Bhatnagar,f.a.sc.

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Srivastava, H.M. A note on certain bilinear and bilateral generating relations for the laguerre polynomial. Proc. Indian Acad. Sci. 74, 299–308 (1971). https://doi.org/10.1007/BF03048401

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