Chu: Reciprocal Formulae on Binomial Convolutions of Hagen-Rothe Type

Chu, Wenchang:
Reciprocal Formulae on Binomial Convolutions of Hagen-Rothe Type
Bollettino dell'Unione Matematica Italiana Serie 9 6 (2013), fasc. n.3, p. 591-605, (English)
pdf (291 Kb), djvu (130 Kb). | MR 3202842

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By means of duplicate inverse series relations, we investigate dual relations of four binomial convolution identities. Four classes of reciprocal formulae on binomial convolutions of Hagen-Rothe type are established. They reflect certain “reciprocity” on the Hagen-Rothe-like convolutions in the sense that each binomial summation involved has no closed form in general, but their sum and difference in pairs do have simple expressions in a single term of binomial coefficients.

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Referenze Bibliografiche