An explicit formula for the linearization coefficients of Bessel polynomials II

preprint2012arXivOpen access

Abstract

In this paper, a single sum formula for the linearization coefficients of the Bessel polynomials is given. In three special cases this formula reduces indeed to either Atia and Zeng's formula (Ramanujan Journal, Doi 10.1007/s11139-011-9348-4) or Berg and Vignat's formulas in their proof of the positivity results about these coefficients (Constructive Approximation, {\bf 27} (2008), 15-32). As a bonus, a formula reducing a sum of hypergeometric functions 3F2_3F_2 to 2F1_2F_1 is obtained.

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