Logarithmic Integrals of Airy Functions
Bernard J. Laurenzi
TL;DR
This paper derives closed-form expressions for integrals involving logarithms of Airy functions, which are relevant in the Thomas-Fermi model of atomic structure, using incomplete Bell polynomials.
Contribution
It introduces a novel method to express these integrals in closed form, advancing analytical techniques in atomic physics.
Findings
Expressed integrals in terms of incomplete Bell polynomials
Provided closed-form solutions for specific integrals in TF theory
Enhanced analytical tools for atomic structure calculations
Abstract
Integrals arising in the Thomas-Fermi (TF) theory of atomic structure and which contain logarithms of the Airy functions have been expressed in terms of the incomplete Bell polynomials. In keeping with the spirit of TF theory closed forms for these integrals are sought.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Mathematical Inequalities and Applications