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I found this amazing formula, which expresses the logarithm of gamma function: $$\ln\Gamma(z)=\frac{1}{2}\ln{(2\pi)}+(z-\frac{1}{2})\ln{z}-z+\sum_{n=1}^{\infty}{\frac{B_{2n}}{2n(2n-1)z^{2n-1}}}$$ Link: http://mathworld.wolfram.com/StirlingsSeries.html

Would anyone give me any hint or just an idea how does one derive this identity? I am pretty familiar with the Stirling approximation of the factorial (Gamma function) which is: $$\Gamma(n+1)\approx\sqrt{2\pi n}\bigg(\frac{n}{e}\bigg)^n$$ I'll be tahnkful for any reasonable suggestions or links where i can find something about this.

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