![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Digamma.png/640px-Digamma.png&w=640&q=50)
Digamma function
Mathematical function / From Wikipedia, the free encyclopedia
For Barnes' gamma function of two variables, see double gamma function.
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function:[1][2][3]
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Digamma.png/320px-Digamma.png)
visualized using domain coloring
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Mplwp_polygamma03.svg/320px-Mplwp_polygamma03.svg.png)
It is the first of the polygamma functions. This function is strictly increasing and strictly concave on ,[4] and it asymptotically behaves as[5]
for complex numbers with large modulus () in the sector
with some infinitesimally small positive constant
.
The digamma function is often denoted as or Ϝ[6] (the uppercase form of the archaic Greek consonant digamma meaning double-gamma).