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Incomplete gamma function
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===Software implementation=== The incomplete gamma functions are available in various of the [[computer algebra system]]s. Even if unavailable directly, however, incomplete function values can be calculated using functions commonly included in [[spreadsheet]]s (and computer algebra packages). In [[Microsoft Excel|Excel]], for example, these can be calculated using the [[gamma function]] combined with the [[gamma distribution]] function. *The lower incomplete function: <math> \gamma(s, x) </math> <code> = EXP(GAMMALN(s))*GAMMA.DIST(x,s,1,TRUE)</code>. *The upper incomplete function: <math> \Gamma(s, x) </math> <code> = EXP(GAMMALN(s))*(1-GAMMA.DIST(x,s,1,TRUE))</code>. These follow from the definition of the [[Gamma distribution#Cumulative distribution function|gamma distribution's cumulative distribution function]]. In [[Python (programming language)|Python]], the Scipy library provides implementations of incomplete gamma functions under {{code|scipy.special}}, however, it does not support negative values for the first argument. The function {{Code|gammainc}} from the mpmath library supports all complex arguments.
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