Mellin transform of quartic products of shifted Airy functions
E.G. Abramochkin, E.V. Razueva
TL;DR
This paper derives a closed-form expression for the Mellin transform of quartic products of shifted Airy functions, including special cases involving logarithms and elliptic integrals, advancing mathematical analysis of these functions.
Contribution
It provides the first explicit closed-form Mellin transform for quartic products of shifted Airy functions, including special cases with known functions.
Findings
Closed-form Mellin transform derived
Special cases expressed with logarithms and elliptic integrals
Enhances analytical tools for Airy function products
Abstract
The Mellin transform of quartic products of shifted Airy functions is evaluated in a closed form. Some particular cases expressed in terms of the logarithm function and complete elliptic integrals special values are presented.
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