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Generalized q-Stirling Numbers and Their Interpolation Functions

Hacer Özden, İsmail Naci Cangül, Yılmaz Şimşek

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Stirling numbers of the second kind, Bernoulli number, Stirling numbers of the first kind, Bell polynomials, Stirling number, Mathematics, Interpolation (computer graphics), Generating function

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