Gauss Digamma Theorem proof?

So, many people know the gamma function, Γ(x). But if you do this -

$\frac{d}{dx} (lnΓ(x))$ ,

you get Ψ(x). The digamma function.

There is a theorem called the "Gauss Digamma Theorem" (Which is very long). This theorem allows one to calculate Ψ( $\frac{a}{b}$ ), a<b

I was wondering if anyone here knew a proof.

#Calculus

Easy Math Editor

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`2 \times 3`	$2 \times 3$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$