Function digamma

In Mathematical, the function digamma or function Psi is defined by

$\backslash \; Psi\; (X)\; =D\; \backslash \; ln\; \{\backslash \; Gamma\; (X)\}=\; \backslash \; frac\; \{\backslash \; Gamma\text{'}\; (X)\}\{\backslash \; Gamma\; (X)\}$

where D is the differential Opérateur.

The function digamma, often also noted $\backslash \; psi\_0\; (X)\; \backslash ,$ or even $\backslash \; psi^0\; (X)\; \backslash ,$, is connected to the harmonic numbers by

$\backslash \; psi\; (N)\; =\; H\_\; \{n-1\}\; -\; \backslash \; gamma\; \backslash ,$

where $H\_\; \{n-1\}\; \backslash ,$ is it (N - 1) - ième harmonic number, and $\backslash \; gamma\; \backslash ,$ is celebrates it Constante of Euler-Mascheroni.

See too

• Function Gamma of Euler

• harmonic Function polygamma
• Number

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