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arXiv · 2610.08422

The Mehler-Fock transform of arbitrary order

Sudhanshu Ranjan·Akhilesh Prasad
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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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Sudhanshu Ranjan, Akhilesh Prasad. 2026-10-06. The Mehler-Fock transform of arbitrary order. https://arxiv.org/abs/2610.08422

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