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Landen-Type Inequality for Bessel Functions

Landen-Type Inequality for Bessel Functions Let u p(x) be the generalized and normalized Bessel function depending on parameters b,c,p and let λ(r) = u p(r2), r ∈} (0,1). Motivated by an open problem of Anderson, Vamanamurthy and Vuorinen, we prove that the Landen-type inequality λ(2√r/(1 + r)) < Cλ(r) holds for all r ∈ (0,1) and C > 1, for certain conditions on the parameters b,c,p. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Landen-Type Inequality for Bessel Functions

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Publisher
Springer Journals
Copyright
Copyright © 2005 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321104
Publisher site
See Article on Publisher Site

Abstract

Let u p(x) be the generalized and normalized Bessel function depending on parameters b,c,p and let λ(r) = u p(r2), r ∈} (0,1). Motivated by an open problem of Anderson, Vamanamurthy and Vuorinen, we prove that the Landen-type inequality λ(2√r/(1 + r)) < Cλ(r) holds for all r ∈ (0,1) and C > 1, for certain conditions on the parameters b,c,p.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

References