Abstract
By using a recent generalization of the Cauchy–Schwarz inequality we obtain several new inequalities for some basic special functions such as beta and incomplete beta functions, gamma, polygamma and incomplete gamma functions, error functions, various kinds of Bessel functions, exponential integral functions, Gauss hypergeometric and confluent hypergeometric functions, elliptic integrals, moment generating functions and the Riemann zeta function. We also apply the generalized Cauchy–Schwarz inequality to some classical integral transforms. All these new inequalities obey the general form f 2 ( x ) ≤ k ( x ) f ( p x + q ) f ( ( 2 − p ) x − q ) , in which p , q are real parameters and k ( x ) is a specific positive function.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
