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.)
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