The Marcum Q function is defined as
Q
M.
{\ displaystyle Q_ {M}}
Q
M.
(
a
,
b
)
=
∫
b
∞
x
(
x
a
)
M.
-
1
exp
(
-
x
2
+
a
2
2
)
I.
M.
-
1
(
a
x
)
d
x
{\ displaystyle 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} \ left (ax \ right) dx}
where the modified Bessel function of the first genus is M-1st order. The Marcum Q function is used, among other things, as a distribution function of the non-central chi-square distribution .
I.
M.
-
1
{\ displaystyle I_ {M-1}}
literature Albert H. Nuttall: Some Integrals Involving the Q M Function. In: IEEE Transactions on Information Theory. No. 21, 1975, ISSN 0018-9448 IEEE Xplore ).
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