MarcumQ
Details

- Mathematical function suitable for both symbolic and numerical evaluation.
for real positive
,
, and
.
- MarcumQ[m,a,b] is an entire function of both a and b with no branch cut discontinuities.
- For a certain special argument, MarcumQ automatically evaluates to exact values.
- MarcumQ can be evaluated to arbitrary numerical precision.
- MarcumQ automatically threads over lists.
Examples
open allclose allBasic Examples (4)
Scope (21)
Numerical Evaluation (4)
Visualization (2)
Plot the MarcumQ function for various parameters:
Function Properties (9)
Real domain of MarcumQ:
Complex domain of MarcumQ:
Approximate function range of :
is an analytic function of
and
for positive integer
:
It has no singularities or discontinuities:
is neither non-increasing nor non-decreasing:
is neither convex nor concave:
TraditionalForm formatting:
Differentiation (2)
Series Expansions (2)
Find the Taylor expansion using Series:
Applications (2)
Amplitude of a signal is modeled by RiceDistribution. Find the probability that the amplitude will exceed its mean value:
Compare the value of the MarcumQ function for large arguments to its asymptotic formula:
Properties & Relations (3)
MarcumQ can be used to compute the SurvivalFunction of SkellamDistribution:
MarcumQ computes the SurvivalFunction of NoncentralChiSquareDistribution:
MarcumQ computes the SurvivalFunction of RiceDistribution:
Text
Wolfram Research (2010), MarcumQ, Wolfram Language function, https://reference.wolfram.com/language/ref/MarcumQ.html.
CMS
Wolfram Language. 2010. "MarcumQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MarcumQ.html.
APA
Wolfram Language. (2010). MarcumQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MarcumQ.html