Discrete index transformations with squares of Bessel functions

Abstract

Discrete analogues of the index transforms with squares of Bessel functions of the first and second kind $J_{\nu }(z),Y_{\nu }(z)$ are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

Keywords:

• Bessel functions
• modified Bessel functions
• Struve functions
• Lommel functions
• Fourier series
• index transforms

AMS subject classifications:

• 45A05
• 44A15
• 42A16
• 33C10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was partially supported by CMUP, which was financed by national funds through FCT (Portugal) under the project with reference UIDB/00144/2020.