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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.