Derivative formulas for Bessel, Struve and Anger-Weber functions

TL;DR

This paper derives formulas for the derivatives of various orders of functions related to Bessel, Struve, and Anger-Weber functions, expanding the mathematical tools available for these special functions.

Contribution

It introduces new derivative formulas for the functions $z^{- u}h_{ u}(z)$ and $z^{ u}h_{ u}(z)$, where $h_{ u}(z)$ is a Bessel, Struve, or Anger--Weber function.

Findings

Derived formulas for derivatives of all orders

Applicable to Bessel, Struve, and Anger--Weber functions

Enhances analytical methods involving these special functions

Abstract

We derive formulas for the derivatives of general order for the functions $z^{-\nu}h_{\nu}(z)$ and $z^{\nu}h_{\nu}(z)$, where $h_{\nu}(z)$ is a Bessel, Struve or Anger--Weber function.