Baricz, Árpád; Bisht, Nitin; Singh, Sanjeev; Vijesh, V. Antony Asymptotic and numerical aspects of the generalized Marcum function of the second kind. (English) Zbl 1499.41095 Appl. Anal. Discrete Math. 16, No. 1, 202-217 (2022). Summary: The asymptotic and numerical behavior of the so-called generalized Marcum function of the second kind is considered. By using some known expansions on the modified Bessel function of the second kind, we deduce the asymptotic expansions for the generalized Marcum function of the second kind for large parameters, and all the expansions are obtained when exactly one parameter is large and others are fixed. We also show numerically that the asymptotic formulas obtained in this paper are good approximations. MSC: 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 30E05 Moment problems and interpolation problems in the complex plane 33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\) Keywords:modified Bessel function of the second kind; asymptotic expansion; generalized Marcum function of the second kind; recurrence relation; Laplace method Software:DLMF; Algorithm 939 PDFBibTeX XMLCite \textit{Á. Baricz} et al., Appl. Anal. Discrete Math. 16, No. 1, 202--217 (2022; Zbl 1499.41095) Full Text: DOI References: [1] Á. Baricz, N. Bisht, S. Singh, V.A. Vijesh: The generalized Marcum function of the second kind: monotonicity patterns and tight bounds., J. Comput. Appl. Math, 382 (2021), Art. 113093. · Zbl 1472.33015 [2] Á. Baricz, N. Bisht, S. Singh, V.A. Vijesh: Bounds for the generalized Marcum function of the second kind., Ramanujan J., 58 (2022), 1-21. doi: 10.1007/s11139-021-00440-9. · Zbl 1509.33023 · doi:10.1007/s11139-021-00440-9 [3] A. Gil, J. Segura, N.M. Temme: Algorithm 939: Computation of the Marcum Q-function. ACM Trans. Math. Software, 40 (3) (2014), Art. 20. · Zbl 1322.65046 [4] S. Nadarajah: A modified Bessel distribution of the second kind., Statistica, 47 (4) (2007), 405-413. · Zbl 1189.62014 [5] F.W.J. Olver, D.W. Lozier, R.F. Boisvert, C.W. Clark (Eds.): NIST Handbook of Mathematical Functions. Cambridge Univ. Press, Cambridge, 2010. · Zbl 1198.00002 [6] R. Wong: Asymptotic approximations of integrals., Academic Press, 1989. · Zbl 0679.41001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.