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The Mehler-Fock transform of arbitrary order
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).
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BibTeX
@misc{ranjan2026mehlerfock,
title = {{The Mehler-Fock transform of arbitrary order}},
author = {Sudhanshu Ranjan and Akhilesh Prasad},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08422},
eprint = {2610.08422},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08422},
}
RIS
TY - UNPB
TI - The Mehler-Fock transform of arbitrary order
AU - Sudhanshu Ranjan
AU - Akhilesh Prasad
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08422
UR - https://arxiv.org/abs/2610.08422
AB - 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).
ER -