伽玛函数（Gamma），也叫欧拉第二积分，是阶乘函数在实数与复数上扩展的一类函数。该函数在分析学、概率论、偏微分方程和组合数学中有重要的应用。与之有密切联系的函数是贝塔函数，也叫第一类欧拉积分，可以用来快速计算同伽马函数形式相类似的积分。
function [Fun_SPC_Gamma](@x float)
returns float
begin
if @x <= 0
return 1
declare @gamma float
set @gamma = 0.577215664901532860606512090
if @x <0.001
return 1.0 / (@x * (1.0 + @gamma * @x));
if @x < 12
begin
declare @y float
set @y =@x
declare @n int
set @n = 0
declare @arg_was_less_than_one bit
if @y < 1.0
set @arg_was_less_than_one = 1
else
set @arg_was_less_than_one = 0
if @arg_was_less_than_one = 1
set @y = @y + 1
else
begin
set @n= cast(Floor(@y) as int) - 1
set @y =@y - @n
end
declare @tbP table
(
id int,
const float
)
insert into @tbP values(1,-1.71618513886549492533811E+0)
insert into @tbP values(2,2.47656508055759199108314E+1)
insert into @tbP values(3,-3.79804256470945635097577E+2)
insert into @tbP values(4,6.29331155312818442661052E+2)
insert into @tbP values(5,8.66966202790413211295064E+2)
insert into @tbP values(6,-3.14512729688483675254357E+4)
insert into @tbP values(7,-3.61444134186911729807069E+4)
insert into @tbP values(8,6.64561438202405440627855E+4)
declare @tbQ table
(
id int,
const float
)
insert into @tbQ values(1,-3.08402300119738975254353E+1)
insert into @tbQ values(2,3.15350626979604161529144E+2)
insert into @tbQ values(3,-1.01515636749021914166146E+3)
insert into @tbQ values(4,-3.10777167157231109440444E+3)
insert into @tbQ values(5,2.25381184209801510330112E+4)
insert into @tbQ values(6,4.75584627752788110767815E+3)
insert into @tbQ values(7,-1.34659959864969306392456E+5)
insert into @tbQ values(8,-1.15132259675553483497211E+5)
declare @num float
declare @den float
set @num = 0
set @den = 1
declare @i int
declare @z float
set @z = @y - 1
set @i = 1
while @i <=8
begin
declare @p float
declare @q float
select
@p = const
from @tbP t
where id = @i
select
@q = const
from @tbQ t
where id = @i
set @num = (@num + @p) * @z
set @den = @den * @z + @q
set @i = @i + 1
end
declare @result float
set @result = @num/@den + 1.0
if @arg_was_less_than_one = 1
begin
set @result = @result/(@y - 1)
end
else
begin
declare @j int
set @j = 0
while @j< @n
begin
set @result = @result * @y
set @y =@y + 1
set @j = @j + 1
end
end
return @result
end
if @x > 171.624
return 1
return Exp(dbo.Fun_SPC_LogGamma(@x))
end
