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EngWiPy
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Homework Statement
I read in a paper that:
[tex]\Gamma\left(c,\,d\frac{x+e}{x-y}\right) = (c-1)!\,exp\left[-d\frac{y+e}{x-y}\right]\,exp[-d]\,\sum_{k=0}^{c-1}\,\sum_{l=0}^k \frac{d^k}{k!}{k\choose l}\left(\frac{y+e}{x-y}\right)^l [/tex]
Homework Equations
But the incomplete gamma function defined in the book of table of integrals and series as:
[tex]\Gamma(1+n,x) = n!\,exp[-x]\,\sum_{k=0}^n \frac{x^m}{m!}[/tex]
The Attempt at a Solution
Applying this we get:
[tex]\Gamma\left(c,\,d\frac{x+e}{x-y}\right) = (c-1)!\, exp\left[-d\frac{x+e}{x-y}\right]\,\sum_{k=0}^{c-1} \frac{d^k}{k!}\,\left(\frac{x+e}{x-y}\right)^k \neq (c-1)!\,exp\left[-d\frac{y+e}{x-y}\right]\,exp[-d]\,\sum_{k=0}^{c-1}\,\sum_{l=0}^k \frac{d^k}{k!}{k\choose l}\left(\frac{y+e}{x-y}\right)^l[/tex]
How did the authors get their result?
Regards
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