Tur\'an type inequalities for regular Coulomb wave functions
\'Arp\'ad Baricz
TL;DR
This paper establishes Turán-type inequalities for regular Coulomb wave functions, utilizing Mittag-Leffler expansions, and explores related properties such as monotonicity of Coulomb zeta functions and zero interlacing.
Contribution
It introduces new Turán-type inequalities for Coulomb wave functions and derives monotonicity and zero interlacing properties using novel Mittag-Leffler expansions.
Findings
Derived Turán inequalities for Coulomb wave functions
Established complete monotonicity of Coulomb zeta functions
Proved interlacing properties of Coulomb wave function zeros
Abstract
Tur\'an, Mitrinovi\'c-Adamovi\'c and Wilker type inequalities are deduced for regular Coulomb wave functions. The proofs are based on a Mittag-Leffler expansion for the regular Coulomb wave function, which may be of independent interest. Moreover, some complete monotonicity results concerning the Coulomb zeta functions and some interlacing properties of the zeros of Coulomb wave functions are given.
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