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On q-deformed Stirling Numbers

Yilmaz Simsek

Abstract


The purpose of this article is to introduce many properties of the q-deformed Stirling numbers of the first and second kinds. Relations between the q-deformed Stirling numbers, the Riemann zeta function and the q-Bernoulli numbers, Euler numbers of higher order and q-Bell numbers are given. Moreover, interpolation function of the q-deformed Stirling numbers of the second kind is defined. Some properties of this function are given. Many identities related to these numbers and function are introduced.

Keywords


(q)-Bernoulli numbers and polynomials, (q)-Bernoulli numbers and polynomials, (q)-Stirling numbers of the first and the second kind, fermionic Stirling numbers of the first and the second kind, (q)-Bell Numbers, Mellin transformation.

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