Question

State and prove Dublication formula ​

Answer 1

Answer:

The duplication formula can be written as

Γ(x)Γ(x+

1

2

)

Γ(2x)

=

Γ(

1

2

)

22x−1

=

√

π

22x−1

.

We want to derive this formula using the Weierstrass definition for the gamma function,

1

Γ(x)

=xeγx

∞

∏

k=1 (1+

x

k

)e−x/k.