Dataplot Vol 2 Vol 1

# TRIGAMMA

Name:
TRIGAMMA (LET)
Type:
Library Function
Purpose:
Compute the trigamma function.
Description:
The digamma function is the logarithmic derivative of the gamma function and is defined as:

$\psi(x) = \frac{\Gamma'(x)} {\Gamma(x)}$

where $$\Gamma$$ is the gamma function and $$\Gamma'$$ is the derivative of the gamma function.

The trigamma function is the derivative of the digamma function and is defined as

$\begin{array}{lcl} \psi_{1}(x) & = & \psi'(x) \\ & = & \frac{d^2}{dx^2} \ln (\Gamma(x)) \\ & = & \sum_{n=0}^{\infty}{\frac{1}{(x+n)^{2}}} \end{array}$

This function is defined for positive numbers.

Syntax:
LET <y> = TRIGAMMA(<x>)             <SUBSET/EXCEPT/FOR qualification>
where <x> is a number, variable or a parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed trigamma values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = TRIGAMMA(1)
LET X2 = TRIGAMMA(X1)
LET X2 = TRIGAMMA(X1-4)
Note:
Dataplot uses the routine DPSIFN from the SLATEC Common Mathematical Library to compute this function. SLATEC is a large set of high quality, portable, public domain Fortran routines for various mathematical capabilities maintained by seven federal laboratories.
Default:
None
Synonyms:
None
Related Commands:
 GAMMA = Compute the gamma function. DIGAMMA = Compute the digamma function. LOGGAMMA = Compute the log (to base e) gamma function.
Reference:
D. E. Amos (1983), "A portable Fortran subroutine for derivatives of the Psi function", Algorithm 610, ACM Transactions on Mathematical Software 9, 4, pp. 494-502.

Abramowitz and Stegun, "Handbook of Mathematical Functions, Applied Mathematics Series, Vol. 55", National Bureau of Standards, 1964 (chapter 6).

Applications:
Special Functions
Implementation Date:
2014/12
Program:

TITLE CASE ASIS
TITLE Trigamma Function
PLOT TRIGAMMA(X) FOR X = 0.01 0.01 10


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Date created: 01/31/2015
Last updated: 01/31/2015