Question

Use Beta and Gamma functions , evaluate ∫

+
∞

Answer 1

Answer:

In mathematics, the beta function, also called the Euler integral of the first kind, is a special function defined by

{\displaystyle \mathrm {B} (x,y)=\int _{0}^{1}t^{x-1}(1-t)^{y-1}\,dt}{\displaystyle \mathrm {B} (x,y)=\int _{0}^{1}t^{x-1}(1-t)^{y-1}\,dt}

for Re x > 0, Re y > 0.

The beta function was studied by Euler and Legendre and was given its name by Jacques Binet; its symbol Β is a Greek capital beta rather than the similar Latin capital B or the Greek lowercase β.

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