Gamma function, show that gamma ( n+1 ) = n gamma n

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In mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers.
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When we first put the values of limit then why do we put the limit to the t^n term but it is out side of the integration part?

anuragsaikia
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Infinity multiply by zero is does not equal to zero sir

lokendrabhatt