Orthogonality relations for conical functions of imaginary order

TL;DR

This paper derives orthogonality relations for conical functions of imaginary order, extending existing relations for associated Legendre functions, and expresses these relations using the Dirac delta function.

Contribution

It introduces new orthogonality relations for conical functions of imaginary order, expanding the mathematical understanding of these special functions.

Findings

Orthogonality relations expressed via Dirac delta function

Extension of relations from associated Legendre functions

Mathematical framework for conical functions of imaginary order

Abstract

Orthogonality relations for conical or Mehler functions of imaginary order are derived and expressed in terms of the Dirac delta function. This work extends recently derived orthogonality relations of associated Legendre functions.