Regularized Gamma Function
المؤلف:
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T
المصدر:
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press
الجزء والصفحة:
pp. 160-161
23-5-2019
1583
Regularized Gamma Function
The regularized gamma functions are defined by
where 
and 
are incomplete gamma functions and 
is a complete gamma function. The function 
is implemented in the Wolfram Language as GammaRegularized[a, 0, z], and 
is implemented as GammaRegularized[a, z].
and 
satisfy the identity
 |
(3)
|
The derivatives of 
and 
are
and the second derivatives are
The integrals are
REFERENCES:
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 160-161, 1992.
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