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Axioms 2013, 2(1), 10-19; doi:10.3390/axioms2010010
Article

Generalized q-Stirling Numbers and Their Interpolation Functions

1,* , 1
 and 2
1 Faculty of Arts and Science, Department of Mathematics, Uludag University, TR-16059, Bursa, Turkey 2 Faculty of Science, Department of Mathematics, University of Akdeniz, TR-07058, Antalya, Turkey
* Author to whom correspondence should be addressed.
Received: 21 November 2012 / Revised: 28 January 2013 / Accepted: 31 January 2013 / Published: 8 February 2013
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Abstract

In this paper, we define the generating functions for the generalized q-Stirling numbers of the second kind. By applying Mellin transform to these functions, we construct interpolation functions of these numbers at negative integers. We also derive some identities and relations related to q-Bernoulli numbers and polynomials and q-Stirling numbers of the second kind.
Keywords: q-Bernoulli numbers and polynomials; generalized q-Stirling numbers of the second kind; q-zeta function q-Bernoulli numbers and polynomials; generalized q-Stirling numbers of the second kind; q-zeta function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Ozden, H.; Cangul, I.N.; Simsek, Y. Generalized q-Stirling Numbers and Their Interpolation Functions. Axioms 2013, 2, 10-19.

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