Tight bounds for the generalized Marcum Q-function

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

In this paper we study the generalized Marcum Q-function of order ν > 0 real, defined byQν (a, b) = frac(1, aν - 1) underover(∫, b, ∞) tν e- frac(t2 + a2, 2) Iν - 1 (a t) dt, where a > 0, b ≥ 0 and Iν stands for the modified Bessel function of the first kind. Our aim is to improve and extend some recent results of Wang to the generalized Marcum Q-function in order to deduce some sharp lower and upper bounds. In both cases b ≥ a and b <a we give the best possible upper bound for Qν (a, b). The key tools in our proofs are some monotonicity properties of certain functions involving the modified Bessel function of the first kind. These monotonicity properties are deduced from some results on modified Bessel functions, which have been used in wave mechanics and finite elasticity.

Original languageEnglish
Pages (from-to)265-277
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume360
Issue number1
DOIs
Publication statusPublished - Dec 1 2009

Fingerprint

Modified Bessel Functions
Bessel functions
Q-function
Bessel function of the first kind
Monotonicity
Finite Elasticity
Mechanics
Upper and Lower Bounds
Deduce
Elasticity
Upper bound

Keywords

  • Complementary error function
  • Generalized Marcum Q-function
  • Lower and upper bounds
  • Marcum Q-function
  • Modified Bessel functions
  • Sharp bounds

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Tight bounds for the generalized Marcum Q-function. / Baricz, A.

In: Journal of Mathematical Analysis and Applications, Vol. 360, No. 1, 01.12.2009, p. 265-277.

Research output: Contribution to journalArticle

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