Turán type inequalities for regular Coulomb wave functions. (English) Zbl 1318.33039
Summary: Turán, Mitrinović-Adamović 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.
MSC:
| 33E15 | Other wave functions |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 33E12 | Mittag-Leffler functions and generalizations |
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
Keywords:
Coulomb wave functions; Mittag-Leffler expansion; Turán; Mitrinović-Adamović; Wilker type inequality; Coulomb zeta functions; complete monotonicity; interlacing property of zerosReferences:
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