# Main source of information for digamma function?

Is there a great source of information for the digamma function $\psi(x)=\frac{d}{dx}\log\Gamma(x)$, $x>0,$ that is not already on the Wikipedia page (http://en.wikipedia.org/wiki/Digamma_function)? In particular, I am interested in exotic identities.

For example, one interesting identity that may seem contrived at first is the following:

$$\log(c/a)\frac{(-1)^b+(-1)^{a+b}}{2a}+\log(a/c)\frac{(-1)^d+(-1)^{c+d}}{2c}$$ $$=\frac{1}{2c}\sum_{n=0}^{2c-1}\frac{(-1)^{nc+d}}{c}\psi\Big(\frac{nc+d}{2c^2}\Big)-\frac{(-1)^{na+b}}{a}\psi\Big(\frac{na+b}{2ac}\Big)$$ $$+\frac{1}{2a}\sum_{n=0}^{2a-1}\frac{(-1)^{na+b}}{a}\psi\Big(\frac{na+b}{2a^2}\Big)-\frac{(-1)^{nc+d}}{c}\psi\Big(\frac{nc+d}{2ac}\Big).$$

Thank you.

Edit: typo.

• – Claude Leibovici Oct 20 '13 at 5:28
• If you have access to a university library with a good collection of math books check out: "Polylogarithms and Associated Functions" by Leonard Lewin . – Alan Oct 20 '13 at 6:49
• Thank you, I will try to find this book. – Maxim Gilula Oct 20 '13 at 14:29