marcumq

mpsci.fun.marcumq(m, a, b)

The Marcum Q function.

The function is defined as

\[Q_M(a, b) = \int_b^{\infty} x \left(\frac{x}{a}\right)^{M-1} \exp\left(-\frac{x^2 + a^2}{2}\right) I_{M-1}(ax)\,dx\]

where \(I_{M-1}(z)\) is the modified Bessel function of order \(M-1\)

See also: cmarcumq()

Returns:

q – The function value.

Return type:

mpmath.mpf

Notes

The function uses numerical integration, so it can be very slow.

Examples

>>> from mpmath import mp
>>> from mpsci.fun import marcumq
>>> mp.dps = 40
>>> marcumq(2, 0.5, 3.0)
mpf('0.07558718754263240906718640000640082605610073')