Explicit formulas associated with some families of generalized Bernoulli and Euler polynomials. (English) Zbl 1402.11034
Summary: In this paper, we propose and derive several new explicit formulas of the generalized Bernoulli and Euler polynomials in terms of the generalized Stirling numbers of the second kind. A study of some families of the modified generalized Euler polynomials yields an interesting algorithm for calculating the generalized Euler polynomials.
Keywords:
algorithm; Bernoulli polynomials and Bernoulli numbers; Euler polynomials and Euler numbers; recurrence relations; generating functions; explicit formulas; Stirling numbers of the first and second kind; Whitney numbers of the second kindReferences:
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