A generic inequality for basic special functions
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS(2023)
Abstract
We introduce a generic inequality of the form f(2)(x) <= f(s)f (2x-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.
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Key words
Cauchy-Schwarz inequality,gamma and beta functions,Gauss and confluent hypergeometric functions,Riemann zeta function,inverse trigonometric functions
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