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Abstract <p>The connection between series involving the harmonic numbers, the polygamma function, its derivatives, and derivatives of hypergeometric functions is investigated. Reduction formulas for derivatives of hypergeometric functions with respect to parameters for integer values of these parameters are obtained. They can be used for simplification of formulas in computer algebra systems.</p>

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Euler Type Series and Reduction Formulas for Derivatives of Hypergeometric Functions with Respect to Parameters

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Yu. A. Brychkov

摘要

Abstract

The connection between series involving the harmonic numbers, the polygamma function, its derivatives, and derivatives of hypergeometric functions is investigated. Reduction formulas for derivatives of hypergeometric functions with respect to parameters for integer values of these parameters are obtained. They can be used for simplification of formulas in computer algebra systems.