Fonksiyona dîgamayê

Fonksiyona digamayê

Fonksiyona dîgamayê an jî vatiniya dîgamayê, li gor termînolojiya matematîkê wek muşteqeke logarîtmîk a fonksiyona gamayê dihê pênasekirin. Ya yekem a ji fonksiyonên polîgamayê ye.

$\psi (x)=\frac{d}{dx}\ln \mathrm{\Gamma }(x)=\frac{{\mathrm{\Gamma }}^{\prime }(x)}{\mathrm{\Gamma }(x)}$

$\psi (n)=H_{n-1}-\gamma$,

$H_n$ - $n$, $\gamma$

$\psi (1-x)-\psi (x)=\pi \cot (\pi x)$

$\psi (x+1)=\psi (x)+\frac{1}{x}$

$\psi (x)=\ln (x)-\frac{1}{2x}+\sum _{n=1}^{\mathrm{\infty }}\frac{\zeta (1-2n)}{x^{2n}}$

$\zeta (x)$

$\psi (x)=\sum _{n=0}^{\mathrm{\infty }}\frac{1}{n+1}\sum _{k=0}^n(-1{)}^k(\genfrac{}{}{0ex}{}{n}{k})\ln (x+k)$

$\frac{{\mathrm{\Gamma }}^{\prime }(p/q)}{\mathrm{\Gamma }(p/q)}=-\gamma -\ln (2q)-\frac{\pi }{2}\cot \left(\frac{\pi p}{q}\right)+2\sum _{0<n<q/2}\cos \left(\frac{2\pi pn}{q}\right)\ln (\sin \left(\frac{\pi n}{q}\right))$,

$p,q$, $0<p<q$.

Çavkanî

• Wikipedia bi zimanê îngilîzî (2010-03-23).

Girêdanên derve

• -{R|http://functions.wolfram.com/GammaBetaErf/PolyGamma}-
• -{R|http://mathworld.wolfram.com/DigammaFunction.html}-
• -{R|http://www.math.sfu.ca/~cbm/aands/page_260.htm}-