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Some integrals involving \(k\) gamma and \(k\) digamma function. (English) Zbl 1460.33002

Summary: In this paper, some new integrals involving \(k\) gamma function and \(k\) digamma function have been established. An integral is established involving \(k\) gamma function, and its special values are discussed. Similarly, some new integrals have been established for \(k\) digamma function, and different elementary function is associated with it for different values of \(k\). A nice representation of the Euler-Mascheroni constant and \(\pi\) in the form of \(k\) digamma function for different values of \(k\) is also obtained.

MSC:

33B15 Gamma, beta and polygamma functions
33C20 Generalized hypergeometric series, \({}_pF_q\)
33C47 Other special orthogonal polynomials and functions
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
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References:

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