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An explicit formula for the generalized Bernoulli polynomials. (English) Zbl 0621.33008
The authors prove a new explicit formula for the generalized Bernoulli polynomials. The main result, expressing these polynomials in terms of the Gaussian hypergeometric function, provides an interesting extension of a representation for the generalized Bernoulli numbers given recently by P. G. Todorov [C. R. Acad. Sci., Paris, Sér. I 301, 665-666 (1985; Zbl 0606.10008)]. This transition and several other connections are also indicated.

MSC:
33C05 Classical hypergeometric functions, \({}_2F_1\)
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
Citations:
Zbl 0606.10008
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References:
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[2] Bailey, W.N, Generalized hypergeometric series, (1935), Cambridge Univ. Press Cambridge/London/New York · Zbl 0011.02303
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[6] Todorov, P.G, Une formule simple explicite des nombres de Bernoulli généralisés, C.R. acad. sci. Paris Sér. I math., 301, 665-666, (1985) · Zbl 0606.10008
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