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Computational Methods and Function Theory

, Volume 5, Issue 2, pp 373–379 | Cite as

Landen-Type Inequality for Bessel Functions

  • Árpád Baricz
Article

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)) < (r) holds for all r ∈ (0,1) and C > 1, for certain conditions on the parameters b,c,p.

Keywords

Landen inequality hypergeometric functions Bessel functions Kummer functions 

2000 MSC

33C05 33C10 33C15 

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References

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Copyright information

© Heldermann  Verlag 2005

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania

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