An explicit formula for the generalized Bernoulli polynomials. (English) Zbl 0621.33008

Srivastava, H. M.; Todorov, Pavel G.

J. Math. Anal. Appl. 130, No. 2, 509-513 (1988).

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

Keywords:

Bernoulli polynomials; Bernoulli numbers

Citations:

Zbl 0606.10008

References:

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[4]	Gould, H. W., Explicit formulas for Bernoulli numbers, Amer. Math. Monthly, 79, 44-51 (1972) · Zbl 0227.10010
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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