Abstract
Closed form expression is established for the cumulative distribution function of the non-central chi _nu '^2(lambda ) probability distribution with integer degrees of freedom nu . This expression includes the Humbert Phi _1 (confluent Appell) hypergeometric function of two variables. A new representation of the Marcum Q_1 function of the first order is obtained, interconnection formula accompanied with a reduction formula for specific, equal unit-parameter case of the Humbert function Phi _1 and the function Phi _3 are established.
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