I'm working through rewriting the gamma function as an infinite product, but my question is just about a specific substitution that was made in my textbook. They took the equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Gamma_ n(z)=\int_0^n t^{z-1} (1-\frac{t}{n}) ^ndt[/tex] for Re(z)>0 and n greater than or equal to 1.

and made the substitution s=t/n. The given result is:

[tex]\Gamma _n(z)=n^z\int_0^1 s^{z-1}(1-s)^nds[/tex]

My question is, why did the upper limit of integration change from n to 1?

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# Substitution changes limits of integration?

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