Wright functions of the second kind and Whittaker functions

TL;DR

This paper explores Wright functions of the second kind, comparing them with Whittaker functions in fractional calculus contexts, and corrects two inaccuracies found in existing literature.

Contribution

It provides a detailed comparison between Wright functions of the second kind and Whittaker functions, and clarifies two erroneous representations in prior research.

Findings

Wright functions of the second kind are relevant in fractional diffusion.

Comparison with Whittaker functions reveals specific similarities and differences.

Identifies and corrects two errors in existing literature.

Abstract

In the framework of higher transcendental functions the Wright functions of the second kind have increased their relevance resulting from their applications in probability theory and, in particular, in fractional diffusion processes. Here, these functions are compared with the well-known Whittaker functions in some special cases of fractional order. In addition, we point out two erroneous representations in the literature.