A generic inequality for basic special functions. Issue 5 (4th May 2023)

• Record Type: Journal Article
• Authors: Masjed-Jamei, Mohammad
• Is Part Of: Integral transforms and special functions. Volume 34:Issue 5(2023)
• Page Start: 384
• Page End: 398
• Publication Date: 2023-05-04
• Subjects: Cauchy–Schwarz inequality -- gamma and beta functions -- Gauss and confluent hypergeometric functions -- Riemann zeta function -- inverse trigonometric functions; Primary: 26D15 -- 26D20 -- Secondary: 33C05 -- 33B15 -- 33B20; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2022.2138379
• Languages: English
• ISSNs: 1065-2469

Abstract

Abstract : We introduce a generic inequality of the form 1 f 2 ( x ) ≤ f ( s ) f ( 2 x − s ) and show that many special functions such as gamma and polygamma functions, Riemann zeta function, beta and incomplete beta functions, Gauss and confluent hypergeometric functions, elliptic integrals and error function satisfy such type of the inequality. We also obtain new inequalities of this type for inverse trigonometric functions arcsin ⁡ x and arctan ⁡ x .