Difference between revisions of "Trigamma"
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(Created page with "The trigamma function $\psi^{(1)}$ is defined by $$\psi^{(1)}(z)=\dfrac{\mathrm{d}^2}{\mathrm{d}z^2} \log \Gamma(z),$$ where $\log \Gamma$ denotes the loggamma function.") |
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$$\psi^{(1)}(z)=\dfrac{\mathrm{d}^2}{\mathrm{d}z^2} \log \Gamma(z),$$ | $$\psi^{(1)}(z)=\dfrac{\mathrm{d}^2}{\mathrm{d}z^2} \log \Gamma(z),$$ | ||
where $\log \Gamma$ denotes the [[loggamma]] function. | where $\log \Gamma$ denotes the [[loggamma]] function. | ||
| + | |||
| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Complexpolygamma,k=1plot.png|Domain coloring of $\psi^{(1)}$. | ||
| + | </gallery> | ||
| + | </div> | ||
| + | |||
| + | =See Also= | ||
| + | [[Digamma]]<br /> | ||
| + | [[Polygamma]]<br /> | ||
| + | |||
| + | =References= | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 03:11, 21 December 2016
The trigamma function $\psi^{(1)}$ is defined by $$\psi^{(1)}(z)=\dfrac{\mathrm{d}^2}{\mathrm{d}z^2} \log \Gamma(z),$$ where $\log \Gamma$ denotes the loggamma function.
Domain coloring of $\psi^{(1)}$.
