Error function inequalities

DOI10.1007/s10444-009-9139-2zbMath1211.33002OpenAlexW1990268629MaRDI QIDQ1960201

Horst Alzer

Publication date: 13 October 2010

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-009-9139-2

zbMATH Keywords

error functionfunctional inequalitiesconvexdifferential inequalitiescompletely monotonicenveloping seriesmean value inequalitiesDhombres-type inequalitiesHölder and Minkowski-type inequalitiesMitrinović-type inequalitiessub- and superadditive

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (13)

Coefficient inequalities for pseudo subclasses of analytical functions related to Petal type domains defined by error function ⋮ A subadditive property of the error function ⋮ On approximating the error function ⋮ A Cauchy-type functional inequality for the error function ⋮ Various results for series expansions of the error functions with the complex variable and some of their implications ⋮ An application of modified sigmoid function to a class of $q-$ starlike and $q-$ convex analytic error functions ⋮ Generalized distribution for analytic function classes associated with error functions and Bell numbers ⋮ Optimal lower and upper bounds for the geometric convex combination of the error function ⋮ New tightness lower and upper bounds for the standard normal distribution function and related functions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On approximating the error function ⋮ A Kuczma-type functional inequality for error and complementary error functions

Cites Work

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• A subadditive property of the gamma function.
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• Mills' ratio: Monotonicity patterns and functional inequalities
• Error Bounds for Asymptotic Expansions of the Ratio of Two Gamma Functions
• Completely monotonic functions
• Convexity according to the geometric mean
• Analytic Inequalities
• On Bounds for the Normal Integral

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