XLeratorDB/statistics Documentation
TRIGAMMA
Updated: 20 January 2017
Use the SQL Server scalar function TRIGAMMA to calculate trigamma(z). Abramowitz and Stegun in Handbook of Mathematical Functions (6.4.1, p.260) defined the polygamma function as:
φ' is known as the trigamma function and is second derivative of the GAMMA function.
Syntax
SELECT [wct].[TRIGAMMA](
<@X, float,>)
Arguments
|
Input Name
|
Definition
|
|
@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.TRIGAMMA(5) as trigamma
This produces the following result.
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.Trigamma(SeriesValue) trigamma
FROM
wct.SeriesFloat(-4,4,.01,NULL,NULL)
This produces the following result.
See Also