Construction of the Digamma Function by Derivative Definition
Michael Morales
TL;DR
This paper derives explicit expressions for the Digamma and Polygamma functions using the derivative definition, highlighting their importance in physics and providing a new analytical approach.
Contribution
It introduces a novel derivation of Digamma and Polygamma functions expressed via hypergeometric functions using the derivative definition.
Findings
Expressions for Digamma and Polygamma functions in terms of hypergeometric functions
Provides a new analytical derivation method for these special functions
Highlights applications in physics and related fields
Abstract
The Digamma and Polygamma functions are important tools in mathematical physics, not only for its many properties but also for the applications in statistical mechanics and stellar evolution. In many textbooks is found its develop almost by the same procedure. In this paper expressions for the Digamma and Polygamma functions, in terms of hypergeometric functions, are found through the derivative definition.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Mathematical Theories