Show that $\frac1{x^p}=\frac1{\Gamma(p)}\int_0^\infty u^{p-1}e^{-xu}\,du$

Asked Oct 30 '19 at 03:21

Active Oct 30 '19 at 03:34

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$$\frac1{x^p}=\frac1{\Gamma(p)}\int_0^\infty u^{p-1}e^{-xu}\,du$$ Hello I am having problems to proof this statment, I really don´t see where to start.

edited Oct 30 '19 at 03:34

Parcly Taxel

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asked Oct 30 '19 at 03:21

Pablo Buitrón

2

You know gamma function, right? Use substitution to change the integral so it becomes like gamma function. In this case, try to let $xu = t$. – Azlif Oct 30 '19 at 03:25
Thanks, now I get it. – Pablo Buitrón Oct 30 '19 at 03:34

Show that $\frac1{x^p}=\frac1{\Gamma(p)}\int_0^\infty u^{p-1}e^{-xu}\,du$

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