Asymptotic and numerical aspects of the generalized Marcum function of the second kind

Applicable Analysis and Discrete Mathematics

article

Arpad Baricz¹  Nitin Bisht²  Sanjeev Singh²  V. Antony Vijesh² 

[1] Department of Economics, Babe¸s-Bolyai University, Cluj-Napoca 400591, Romania, Institute of Applied Mathematics, Obuda University;Department of Mathematics, Indian Institute of Technology Indore

关键词: Modified Bessel function of the second kind;    Asymptotic expansion;    Generalized Marcum function of the second kind;    Recurrence relation;    Laplace method.;   

DOI  :  10.2298/AADM201001008B

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

The asymptotic and numerical behavior of the so-called generalized Marcumfunction of the second kind is considered. By using some known expansionson the modified Bessel function of the second kind, we deduce the asymptoticexpansions for the generalized Marcum function of the second kind for largeparameters, and all the expansions are obtained when exactly one parameteris large and others are fixed. We also show numerically that the asymptoticformulas obtained in this paper are good approximations.

【 授权许可】

Unknown