Analytic computations of digamma function using some new identities

TL;DR

This paper introduces new identities for the digamma function, enabling more straightforward computation of its values at fractional orders, advancing theoretical understanding and computational methods.

Contribution

The paper presents novel identities for the digamma function and demonstrates their use in efficiently computing its fractional values.

Findings

Derived new identities for the digamma function

Computed fractional order digamma values using these identities

Enhanced methods for digamma function evaluation

Abstract

Motivated by rigorous development in the theory of digamma functions, we have first derived some new identities for the digamma function, and then computed the values of digamma function for the fractional orders using these identities conveniently.