The

Digamma Function is a

mathematical function defined as the

logarithmic derivative of the

Gamma Function. It is represented by the

greek letter

digamma, which is similar to a

psi:

**Ψ**.

Viewed on a graph, the Digamma Function resembles the tangent function for z < 0 and a less steep logarithmic function for z > 0. It is undefined at negative integers and zero.

The nth derivative of Ψ(z) is called the polygamma function, denoted ψ_{n}(z). The digamma function itself is sometimes written ψ_{0}, or just ψ.

The digamma function is sometimes used as the logarithmic derivative of the factorial function, written as F(z) = d/dz ln z!. Since the Gamma Function is essentially the factorial function for natural numbers expanded to real and complex numbers, the two Digamma Functions are related: F(z) = ψ_{0} (z+1).

Harmonic numbers can be described as the sum of the Digamma Function and the Euler-Mascheroni constant.

*Source: http://mathworld.wolfram.com/DigammaFunction.html*

Notation note: I couldn't find a character for digamma, so I used a psi. The digamma has bars on the top and bottom of the vertical line. If anyone knows how to put a digamma in, let me know, and I'll fix it. Also, the upper and lower case psis look very similar.