GAMMA

Updated 2024-03-08 14:31:07.503000

Syntax

SELECT [westclintech].[wct].[GAMMA] (
   <@Z, float,>)

Use the scalar function GAMMA to calculate Γ(z). The GAMMA function can be defined as a definite integral for ℜ[z] > 0.

\Gamma(z) = \int_0^\infty t^{z-1} e^{-t}\text{ d}t, \ \qquad \Re(z) > 0\

The value of interest.

float

Gamma is undefined for negative integers.

Gamma is undefined at zero.

Example #1

SELECT wct.GAMMA(2.5) as Gamma;

This produces the following result.

{"columns":[{"field":"Gamma","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"Gamma":"1.32934038817914"}]}

Example #2

SELECT wct.GAMMA(-3.75) as Gamma;

This produces the following result.

{"columns":[{"field":"Gamma","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"Gamma":"0.267866128861417"}]}

Example #3

The following SQL can be run using the SeriesFloat function to create GAMMA values from -4 to 4 which can then be pasted into Excel and graphed.

SELECT z,

       wct.GAMMA(z) as Gamma

FROM

(

    SELECT SeriesValue as z

    FROM wct.SeriesFloat(-4, 4, 0.01, NULL, NULL)

) n;

This produces the following result.