New properties of Special Functions and applications
Vagner Jikia, Ilia Lomidze
TL;DR
This paper introduces new mathematical properties of special functions, including Mellin transforms, hypergeometric functions, and Legendre functions, with applications demonstrated in quantum mechanics involving charged particles.
Contribution
It presents novel results on Mellin transforms, hypergeometric functions, and Legendre functions, and applies these findings to quantum mechanics problems.
Findings
New Mellin transform formulas derived
Connections between Legendre functions established
Applications demonstrated in quantum mechanics of charged particles
Abstract
We have derived some new results for the Mellin transform formulas, as well as for the Gauss hypergeometric function. Also, we have found the connection between the Legendre functions of the second kind. Some of the results obtained we used in quantum mechanics of two charged particles of a continuous spectrum.
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Taxonomy
TopicsMathematical functions and polynomials · Electromagnetic Scattering and Analysis · Fractional Differential Equations Solutions