On Cauchy Numbers and Their Generalizations

Authors : Levent KARGIN

Pages : 456-474

Doi:10.35378/gujs.604550

View : 12 | Download : 4

Publication Date : 2020-06-01

Article Type : Research Paper

Abstract :This paper is concerned with both kinds of the Cauchy numbers and their generalizations. Taking into account Mellin derivative, we relate p-Cauchy numbers of the second kind with shifted Cauchy numbers of the first kind, which yields new explicit formulas for the Cauchy numbers of the both kind. We introduce a generalization of the Cauchy numbers and investigate several properties, including recurrence relations, convolution identities and generating functions. In particular, these results give rise to new identities for Cauchy numbers. 
Keywords : Cauchy numbers, Poly Cauchy numbers, p Cauchy numbers, Generating function, Recurrence relations