Digamma Function/Examples

Examples of Digamma Function

Example: $\map \psi {\dfrac 1 6}$

$\map \psi {\dfrac 1 6} = -\gamma - 2 \ln 2 - \dfrac 3 2 \ln 3 - \dfrac {\pi \sqrt 3} 2$

Example: $\map \psi {\dfrac 1 4}$

$\map \psi {\dfrac 1 4} = -\gamma - 3 \ln 2 - \dfrac \pi 2$

Example: $\map \psi {\dfrac 1 3}$

$\map \psi {\dfrac 1 3} = -\gamma - \dfrac 3 2 \ln 3 - \dfrac \pi {2 \sqrt 3}$

Example: $\map \psi {\dfrac 1 2}$

$\map \psi {\dfrac 1 2} = -\gamma - 2 \ln 2$

Example: $\map \psi {\dfrac 2 3}$

$\map \psi {\dfrac 2 3} = -\gamma - \dfrac 3 2 \ln 3 + \dfrac \pi {2 \sqrt 3}$

Example: $\map \psi {\dfrac 3 4}$

$\map \psi {\dfrac 3 4} = -\gamma - 3 \ln 2 + \dfrac \pi 2$

Example: $\map \psi {\dfrac 5 6}$

$\map \psi {\dfrac 5 6} = -\gamma - 2 \ln 2 - \dfrac 3 2 \ln 3 + \dfrac {\pi \sqrt 3} 2$

Example: $\map \psi 1$

$\map \psi 1 = -\gamma$

Example: $\map \psi {\dfrac 3 2}$

$\map \psi {\dfrac 3 2} = -\gamma - 2 \ln 2 + 2$

Example: $\map \psi {\dfrac 4 3}$

$\map \psi {\dfrac 4 3} = -\gamma - \dfrac 3 2 \ln 3 - \dfrac \pi {2 \sqrt 3} + 3$

Example: $\map \psi {\dfrac 5 4}$

$\map \psi {\dfrac 5 4} = -\gamma - 3 \ln 2 - \dfrac \pi 2 + 4$

Example: $\map \psi {\dfrac 7 6}$

$\map \psi {\dfrac 7 6} = -\gamma - 2 \ln 2 - \dfrac 3 2 \ln 3 - \dfrac {\pi \sqrt 3} 2 + 6$

Example: $\map \psi 2$

$\map \psi 2 = -\gamma + 1$