Question

Show that u=r+gamma






















M

Answer 1

Explanation:

Prove that

Γ(p)×Γ(1−p)=

π

sin(pπ)

,∀p∈(0,1)

With

Γ(p)=∫

∞

0

xp−1e−xdx

My tried:

We have

B(p,q)=∫

1

0

xp−1(1−x)q−1dx=

Γ(p)×Γ(q)

Γ(p+q)

Hence

B(p,1−p)=

Γ(p)×Γ(1−p)

Γ(1)

=Γ(p)×Γ(1−p)=∫

1

0

xp−1(1−x)−pdx

But, come here I don't know how :((