# Is the digamma function close to 0 for large arguments?

1. Jul 11, 2015

### Judyxcheng

1. The problem statement, all variables and given/known
I have taken the limit of both sides of an equation for x going toward infinity. There is a digamma (psi(x)) function on the RHS, and the limit of the term is supposed to be (at least close to) 0. Thus, the term can cancel out.

My professor said that indeed, the digamma function is supposed to be around 0 for large arguments and he wants me to justify that with the digamma function's integral form. However, when I research digamma online, it appears to slowly diverge or converge to a number larger than 0. Can someone clarify this?

2. Relevant equations

Integral form of digamma function, found here where it says "The digamma function satisfies": http://mathworld.wolfram.com/DigammaFunction.html

2. Jul 11, 2015

### Staff: Mentor

It does not go to zero, but it grows only as fast as a logarithm, you can see that based on the recurrence relation.