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Zbl 1013.33002
Paris, R.B.
A uniform asymptotic expansion for the incomplete gamma function. (English)
[J] J. Comput. Appl. Math. 148, No.2, 323-339 (2002). ISSN 0377-0427

A new uniform asymptotic expansion is given for the incomplete gamma function $\Gamma(a,z)$ valid for large $z$. The expansion is compared with one developed by the reviewer [SIAM J. Math. Anal. 10, 757-766 (1979; Zbl 0412.33001)]. The coefficients of the new expansion are simpler to evaluate near the transition point $a=z$, the domain of validity for the complex parameters $a$ and $z$ is smaller. In the new expansion the error function again gives the main approximation, higher terms are related with the error function (and with parabolic cylinder functions). Numerical examples are given to illustrate the accuracy of the expansion.
[N.M.Temme (Amsterdam)]

MSC 2000:: *33B20 Incomplete beta and gamma functions

Keywords: incomplete gamma function; uniform asymptotic expansion

Citations: Zbl 0412.33001

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