Juan L. González-Santander, Fernando Sánchez Lasheras
Published 2023-03-24Version 1
We calculate some infinite sums containing the digamma function in closed-form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as parameter differentiation formulas for the beta incomplete function, reduction formulas of $_{3}F_{2}$ hypergeometric functions, or a definite integral which does not seem to be tabulated in the most common literature. As an application of some sums involving the digamma function, we have calculated some redution formulas for the parameter differentiation of the Mittag-Leffler function and the Wright function.
High-order derivatives of the Bessel functions with an application
Limit formulas for ratios of derivatives of the gamma and digamma functions at their singularities
Uniform enclosures for the phase and zeros of Bessel functions and their derivatives
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