§8.15 Sums

Notes:: See Tricomi (1950b).
Keywords:: incomplete gamma functions
Permalink:: http://dlmf.nist.gov/8.15

8.15.1 $\mathop{\gamma\/}\nolimits\!\left(a,\lambda x\right)=\lambda^{a}\sum _{{k=0}}^{\infty}\mathop{\gamma\/}\nolimits\!\left(a+k,x\right)\frac{(1-\lambda)^{k}}{k!}.$

Symbols:: $!$ : $n!$ : factorial, $\mathop{\gamma\/}\nolimits\!\left(a,z\right)$ : incomplete gamma function, $x$ : real variable, $a$ : parameter and $k$ : nonnegative integer
Permalink:: http://dlmf.nist.gov/8.15.E1
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For sums of infinite series whose terms include incomplete gamma functions, see Prudnikov et al. (1986b, §5.2).