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.


33C05 Classical hypergeometric functions, \({}_2F_1\)
11B39 Fibonacci and Lucas numbers and polynomials and generalizations


Zbl 0606.10008
Full Text: DOI


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