Thursday, September 25, 2008

Fun with the digamma function

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


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.