Digamma function

In mathematics, the digamma function is defined by

<math>\psi(x) =D \ln{\Gamma(x)}= \frac{\Gamma'(x)}{\Gamma(x)}<math>

where D is the differential operator.

The digamma function, often notated 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