ACTA issues

Poly-Cauchy polynomials and generalized Bernoulli polynomials

Takao Komatsu, Genki Shibukawa

Acta Sci. Math. (Szeged) 80:3-4(2014), 373-388

Abstract. We introduce a new type of `poly-Cauchy polynomials' defined by a certain generating function. These polynomials are generalizations of the classical Cauchy polynomials and poly-Cauchy numbers. We give their explicit expression and prove basic properties; the addition formula, iterated integral expression, differential relations and recurrence formula. We also give new type zeta functions associated with the poly-Cauchy polynomials.

DOI: 10.14232/actasm-013-761-9

AMS Subject Classification (1991): 05A15, 11B68, 11B75, 11M41

Keyword(s): generalized Bernoulli polynomials, poly-Bernoulli numbers, zeta functions, poly-Cauchy numbers, poly-Cauchy polynomials

Received February 13, 2013, and in revised form January 7, 2014. (Registered under 11/2013.)