Generating functions via integral transforms

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In this paper, we use some integral transforms to derive, for a polynomial sequence {Pn (x)}n ≥ 0, generating functions of the type Gγ (x, t) = ∑n = 0∞ γn Pn (x) tn, starting from a generating function of type G (x, t) = ∑n = 0∞ Pn (x) tn, where {γn}n ≥ 0 is a real numbers sequence independent on x and t. That allows us to unify the treatment of a generating function problem for many well-known polynomial sequences in the literature. © 2006 Elsevier Inc. All rights reserved.




Ben Cheikh, Y., & Lamiri, I. (2007). Generating functions via integral transforms. Journal of Mathematical Analysis and Applications, 331(2), 1200–1229.

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