DIGAMMA

Updated 2024-03-07 21:27:04.713000

Syntax

SELECT [westclintech].[wct].[DIGAMMA](
   <@X, float,>)

Description

Use the scalar function DIGAMMA to calculate digamma(z). Abramowitz and Stegun in Handbook of Mathematical Functions (6.3.1, p.258) defined the digamma function as:

\psi(z) = \frac{\mathrm{d}}{\mathrm{d}z}\ln\Gamma(z) = \frac{\Gamma'(z)}{\Gamma(z)}

Arguments

@X

The value of interest.

Return Type

float

Remarks

When @X is a negative integer NULL is returned.

When @X = 0 zero is returned

Examples

Example #1

In the example we evaluate the function at x = 5.

SELECT wct.DIGAMMA(5) as psi;

This produces the following result.

{"columns":[{"field":"psi","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"psi":"1.5061176684318"}]}

Example #2

In this example we use the SeriesFloat function from the XLeratorDB math library to generate a series on numbers from -4 to 4 in steps of .01, calculate the psi value for each number in the series, paste the results to Excel and create a simple graph of the function for the range.

SELECT SeriesValue as z,

       wct.Digamma(SeriesValue) psi

FROM wct.SeriesFloat(-4, 4, .01, nULL, NULL);