`DigammaFunction(z)`, rendered as $\psi\!\left(z\right)$, represents the digamma function of argument $z$.

`DigammaFunction(z, m)`, rendered as $\psi^{(m)}\!\left(z\right)$, represents the order $m$ derivative of the digamma function of argument $z$. This is also known as the polygamma function of order $m$ and argument $z$. The case $m = 1$ (rendered as $\psi'\!\left(z\right)$ ) is sometimes called the trigamma function, $m = 2$ the tetragamma function, etc.

Definitions:

Fungrim symbol | Notation | Short description |
---|---|---|

DigammaFunction | $\psi\!\left(z\right)$ | Digamma function |

Source code for this entry:

Entry(ID("f1527d"), SymbolDefinition(DigammaFunction, DigammaFunction(z), "Digamma function"), Description(SourceForm(DigammaFunction(z)), ", rendered as", DigammaFunction(z), ", represents the digamma function of argument", z, "."), Description(SourceForm(DigammaFunction(z, m)), ", rendered as", DigammaFunction(z, m), ", represents the order", m, "derivative of the digamma function of argument", z, ". ", "This is also known as the polygamma function of order", m, "and argument", z, ". ", "The case", Equal(m, 1), "(rendered as ", DigammaFunction(z, 1), ") is sometimes called the trigamma function, ", Equal(m, 2), "the tetragamma function, etc."))