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Landen-Type Inequality for Bessel Functions

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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.

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References

  1. G. Almkvist and B. Berndt, Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, π, and the Ladies Diary, Amer. Math. Monthly 95 (1988), 585–608.

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  2. G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen, Hypergeometric functions and elliptic integrals, in: Current Topics in Analytic Function Theory, H. M. Srivastava and S. Owa (eds.), pp. 48–85, World Scientific, Singapore/London, 1992.

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  3. Á. Baricz, Geometric properties of generalized Bessel functions, manuscript.

  4. S. Ponnusamy and M. Vuorinen, Asymptotic expansions and inequalities for hypergeometric functions, Mathematika 44 (1997), 43–64.

    Article  MathSciNet  Google Scholar 

  5. S. L. Qiu and M. Vuorinen, Landen inequalities for hypergeometric functions, Nagoya Math. J. 154 (1999), 31–56.

    MathSciNet  MATH  Google Scholar 

  6. G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1962.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Str. M. Kogălniceanu 1, RO-400084, Cluj-Napoca, Romania

    Árpád Baricz

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  1. Árpád Baricz
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Correspondence to Árpád Baricz.

Additional information

Work partially supported by the Institute of Mathematics, University of Debrecen, Hungary.

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Baricz, Á. Landen-Type Inequality for Bessel Functions. Comput. Methods Funct. Theory 5, 373–379 (2006). https://doi.org/10.1007/BF03321104

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  • DOI: https://doi.org/10.1007/BF03321104

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