State and prove Dublication formula
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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.
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