Turán-Type Inequalities for Some Lommel Functions of the First Kind

DOI10.1017/S0013091515000413zbMath1362.33007arXiv1308.6477OpenAlexW3099164377MaRDI QIDQ2976213

Stamatis Koumandos, Árpád Baricz

Publication date: 28 April 2017

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.6477

zbMATH Keywords

infinite product representationTuran-type inequalitiesLaguerre-Polya classzeros of Lommel functions of the first kindLommel functions of the first kindmonotone form of l'hospital's rule

Mathematics Subject Classification ID

Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Trigonometric polynomials, inequalities, extremal problems (42A05) Exponential and trigonometric functions (33B10)

Related Items (17)

On a Stirling-Whitney-Riordan triangle ⋮ Turán type inequalities for Struve functions ⋮ Bounds for an integral involving the modified lommel function of the first kind ⋮ Unnamed Item ⋮ Univalence and convexity conditions for certain integral operators associated with the Lommel function of the first kind ⋮ On the characterization properties of certain hypergeometric functions in the open unit disk ⋮ Radii of starlikeness and convexity of some entire functions ⋮ Functional inequalities and monotonicity results for modified Lommel functions of the first kind ⋮ Geometric properties of some Lommel and Struve functions ⋮ Radii of uniform convexity of Lommel and Struve functions ⋮ Positive trigonometric integrals associated with some Lommel functions of the first kind ⋮ Close-to-convexity of some special functions and their derivatives ⋮ On the log-concavity of the fractional integral of the sine function ⋮ Radii of starlikeness of some special functions ⋮ A generalized Eulerian triangle from staircase tableaux and tree-like tableaux ⋮ Inequalities for some integrals involving modified Lommel functions of the first kind ⋮ Bounds for modified Lommel functions of the first kind and their ratios

Cites Work

• Unnamed Item
• Jensen polynomials and the Turán and Laguerre inequalities
• Necessary and sufficient conditions and the Riemann hypothesis
• Inequalities for quasiconformal mappings in space
• On the number of nonreal zeros of real entire functions and the Fourier-Pólya conjecture
• Turán type inequalities for Tricomi confluent hypergeometric functions
• The zeros of certain Lommel functions
• Positive Integrals of Bessel Functions
• Turán type inequalities for the partial sums of the generating functions of Bernoulli and Euler numbers
• On an inequality of P. Turán concerning Legendre polynomials
• On inequalities of the Turán type

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