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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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