Inequalities for the one-dimensional analogous of the Coulomb potential

A. Baricz, Tibor K. Pogány

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper our aim is to present some monotonicity and convexity properties for the one dimensional regularization of the Coulomb potential, which has applications in the study of atoms in magnetic fields and which is in fact a particular case of the Tricomi confluent hypergeometric function. Moreover, we present some Turán type inequalities for the function in the question and we deduce from these inequalities some new tight upper bounds for the Mills ratio of the standard normal distribution.

Original languageEnglish
Pages (from-to)53-67
Number of pages15
JournalActa Polytechnica Hungarica
Volume10
Issue number7
Publication statusPublished - 2013

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Normal distribution
Magnetic fields
Atoms

Keywords

  • Bounds
  • Functional inequalities
  • Gaussian integral
  • Log-convexity and geometrical convexity
  • Mills' ratio
  • Regularization of the Coulomb potential
  • Turán type inequalities

ASJC Scopus subject areas

  • General
  • Engineering(all)

Cite this

Inequalities for the one-dimensional analogous of the Coulomb potential. / Baricz, A.; Pogány, Tibor K.

In: Acta Polytechnica Hungarica, Vol. 10, No. 7, 2013, p. 53-67.

Research output: Contribution to journalArticle

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