# polygamma

(0.001 seconds)

## 9 matching pages

##### 1: 5.15 Polygamma Functions
###### §5.15 Polygamma Functions
The functions $\psi^{(n)}\left(z\right)$, $n=1,2,\dots$, are called the polygamma functions. In particular, $\psi'\left(z\right)$ is the trigamma function; $\psi''$, $\psi^{(3)}$, $\psi^{(4)}$ are the tetra-, penta-, and hexagamma functions respectively. … For $B_{2k}$ see §24.2(i). …
##### 3: 5.21 Methods of Computation
For the left half-plane we can continue the backward recurrence or make use of the reflection formula (5.5.3). Similarly for $\ln\Gamma\left(z\right)$, $\psi\left(z\right)$, and the polygamma functions. …
##### 5: 5.22 Tables
###### §5.22(ii) Real Variables
Abramowitz and Stegun (1964, Chapter 6) tabulates $\Gamma\left(x\right)$, $\ln\Gamma\left(x\right)$, $\psi\left(x\right)$, and $\psi'\left(x\right)$ for $x=1(.005)2$ to 10D; $\psi''\left(x\right)$ and $\psi^{(3)}\left(x\right)$ for $x=1(.01)2$ to 10D; $\Gamma\left(n\right)$, $\ifrac{1}{\Gamma\left(n\right)}$, $\Gamma\left(n+\tfrac{1}{2}\right)$, $\psi\left(n\right)$, $\operatorname{log}_{10}\Gamma\left(n\right)$, $\operatorname{log}_{10}\Gamma\left(n+\tfrac{1}{3}\right)$, $\operatorname{log}_{10}\Gamma\left(n+\tfrac{1}{2}\right)$, and $\operatorname{log}_{10}\Gamma\left(n+\tfrac{2}{3}\right)$ for $n=1(1)101$ to 8–11S; $\Gamma\left(n+1\right)$ for $n=100(100)1000$ to 20S. …
##### 6: Software Index
 ✓ ✓ Open Source With Book Commercial … 5.24(iii) $\psi\left(x\right)$, $\psi^{(n)}\left(x\right)$, $x\in\mathbb{R}$ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 5.24(iv) $\Gamma\left(z\right)$, $\psi\left(z\right)$, $\psi^{(n)}\left(z\right)$, $z\in\mathbb{C}$ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ …
##### 7: Bibliography
• V. S. Adamchik (1998) Polygamma functions of negative order. J. Comput. Appl. Math. 100 (2), pp. 191–199.
• ##### 8: Bibliography K
• E. Konishi (1996) Calculation of complex polygamma functions. Sci. Rep. Hirosaki Univ. 43 (1), pp. 161–183.
• ##### 9: Bibliography B
• K. O. Bowman (1984) Computation of the polygamma functions. Comm. Statist. B—Simulation Comput. 13 (3), pp. 409–415.