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# Fun with the digamma function

*September 25, 2008*

Let *a* ≈ 0.46163 be the positive real number that minimizes the factorial, *x*!. Then Euler’s constant γ is given by

and

where ζ(*s*) is the Riemann zeta function. Both formulas follow trivially from the properties of the digamma function, but if I didn’t know that, I’d find them pretty neat.