Year: 2026
Type: preprint
Abstract: In this paper, we construct the Mehler-Fock transform of arbitrary order MF(mu,k) by removing the restriction Re(mu) > -1/2 with the help of a positive integer k such that Re(mu+k) > -1/2 and obtain some transformation formulae based on the differential operator M(mu)N(mu). Furthermore, we define the Mehler-Fock translation and convolution operators of arbitrary order and demonstrate that the factorization property for the convolution holds in the test function space H(mu).
Source: arXiv (Cornell University)
Authors: Ranjan, Sudhanshu, Prasad, Akhilesh
Institution: Indian Institute of Technology Dhanbad
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220980212