engleski

New expression for CDF of χν'2(λ) distribution and Marcum Q1 function

Closed form expression is established for the cumulative distribution function of the non– central χν'2(λ) probability distribution with integer degrees of freedom ν. This expression includes the Humbert Φ1 (confluent Appell) hypergeometric function of two variables. A new representation of the Marcum Q1 function of the first order is obtained, interconnection formula accompanied with a reduction formula for specific, equal unit–parameter case of the Humbert function Φ1 and the function Φ3 are established.

CDF of non–central χ 2 distribution ; Marcum Q1 function ; Modified Bessel function of the first kind ; Humbert Φ1 and Φ3 functions ; Goldstein I(ξ, η) function

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