A generic inequality for basic special functions

We introduce a generic inequality of the form 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...

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Published in:Integral transforms and special functions Vol. 34; no. 5; pp. 384 - 398
Main Author: Masjed-Jamei, Mohammad
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.05.2023
Taylor & Francis Ltd
Subjects:
Cauchy-Schwarz inequality
Elliptic functions
Error functions
gamma and beta functions
Gauss and confluent hypergeometric functions
Hypergeometric functions
inverse trigonometric functions
Primary: 26D15
Riemann zeta function
Secondary: 33C05
Trigonometric functions
ISSN:1065-2469, 1476-8291
Online Access:Get full text
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Abstract We introduce a generic inequality of the form 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 and .
AbstractList We introduce a generic inequality of the form 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 and .
We introduce a generic inequality of the formand 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 and .
Author Masjed-Jamei, Mohammad
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Snippet We introduce a generic inequality of the form and show that many special functions such as gamma and polygamma functions, Riemann zeta function, beta and...
We introduce a generic inequality of the formand show that many special functions such as gamma and polygamma functions, Riemann zeta function, beta and...
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SubjectTerms Cauchy-Schwarz inequality
Elliptic functions
Error functions
gamma and beta functions
Gauss and confluent hypergeometric functions
Hypergeometric functions
inverse trigonometric functions
Primary: 26D15
Riemann zeta function
Secondary: 33C05
Trigonometric functions
Title A generic inequality for basic special functions
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