Digamma function

In mathematics, the digamma function is defined by

<math>\psi(x) =\frac{d}{dx} \ln{\Gamma(x)}= \frac{\Gamma'(x)}{\Gamma(x)}.<math>

The digamma function, often denoted also ψ₀(x) or even ψ⁰(x), is related to the harmonic numbers in that

<math>\psi(n) = H_{n-1}-\gamma<math>

where H_n−1 is the (n−1)th harmonic number, and γ is the well-known Euler-Mascheroni constant.

Also see

• Gamma function
• Polygamma function
• Harmonic number