On higher derivatives of the Bessel and related functions

Abstract

Closed expressions for the coefficients and in the formula

are derived, where W _ν(z) denotes the Bessel functions J _ν(z) and I _ν(z) or the Macdonald function K _ν(z). Similar results for the Airy functions Ai(z) and Bi(z) and Struve functions H _ν(z) and L _ν(z) are obtained.

Keywords:

• special functions
• Bessel function
• Airy function
• Struve function
• differentiation
• derivatives

2010 Mathematics Subject Classification::

• C3310

Acknowledgements

This work was supported by the Russian Foundation for Fundamental Research under Project 10-07-00040-a.