Some trigonometric integrals involving the log gamma and the digamma function
Donal F. Connon
TL;DR
This paper evaluates new integrals involving the log gamma and digamma functions combined with trigonometric and hyperbolic functions, expanding the set of known integral formulas.
Contribution
It introduces and evaluates several new integrals and series involving the log gamma and digamma functions with trigonometric and hyperbolic functions.
Findings
Derived new integral formulas involving log gamma and digamma functions.
Evaluated series related to these integrals.
Expanded the mathematical understanding of these special functions.
Abstract
This paper considers various integrals where the integrand includes the log gamma function (or its derivative, the digamma function) multiplied by a trigonometric or hyperbolic function. Some apparently new integrals and series are evaluated.
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Taxonomy
TopicsMathematical functions and polynomials · Advanced Mathematical Identities · Mathematical Inequalities and Applications