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Yıldırım, Emrah; Ege, İncı

On \(k\)-analogues of digamma and polygamma functions. (English) Zbl 1424.33007

J. Class. Anal. 13, No. 2, 123-131 (2018).
Summary: In this work, we obtain some integral representations of \(k\)-analogue of classical digammafunction \(\Psi(x)\). Then by using the concepts of neutrix and neutrix limit, we generalize the \(k\)-digamma function \(\Psi_k(x)\) and the \(k\)-polygamma function \(\Psi_k^{(r)}(x)\) for all real values of \(x\), \(r\in \mathbb N\) and \(k>0\). Also, further results are given.

Cited in 3 Documents

MSC:

33B15 Gamma, beta and polygamma functions
33D05 \(q\)-gamma functions, \(q\)-beta functions and integrals

Keywords:

digamma function; polygamma function; \(k\)-digamma function; \(k\)-polygamma function; neutrix
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References:

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