fredrikj.net / blog /

# 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.

fredrikj.net | Blog index | RSS feed | Follow me on Twitter | Become a sponsor