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An extension of the Hille-Hardy formula

Author: H. M. Srivastava
Journal: Math. Comp. 23 (1969), 305-311
MSC: Primary 33.20
MathSciNet review: 0243132
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Abstract: While attempting to give extensions of the well-known Hille-Hardy formula for the generalized Laguerre polynomials $ \{ {L_n}^{(\alpha )}(x)\} $ defined by

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

, the author applies here certain operational techniques and the method of finite mathematical induction to derive several bilinear generating functions associated with various classes of generalized hypergeometric polynomials. It is observed that the earlier works of Brafman [2], [3], [4], Chaundy [5], Meixner [12], Weisner [16], and others quoted in the literature, are only specialized or limiting forms of the results presented here.

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Article copyright: © Copyright 1969 American Mathematical Society

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