(Beta function) Derive the result for p > 0, q > 0; B(p,q) is known as the beta func...

(Beta function) Derive the result

for p > 0, q > 0; B(p,q) is known as the beta function. HINT: Putting x = u2 in

show that

Regarding the latter as a double integral in a Cartesian u, υ plane, change from u, υ to polar coordinates r, θ Making one more change of variables in each integral, the r integral gives Γ(p + q) and the θ integral gives B(p, q).