Usage Notes
The notation used in this chapter follows that of Abramowitz and Stegun (1964).
The following is a table of the functions defined in this chapter:
FAC
n! = Γ(n + 1)
BINOM
n!/m!(n - m)!, 0 m n
GAMMA
GAMR
1/Γ(x)
ALNGAM
ln ǀΓ(x)ǀ,  0, -1, -2,
ALGAMS
ln ǀΓ(x)ǀ and sign Γ(x), x 0, -1, -2,
GAMI
GAMIC
GAMIT
*(a, x) = (x-a/ Γ(a))(a, x), x 0
PSI
ψ(x) = Γ´(x)/ Γ(x), x 0, -1, -2,
PSI1
ψ1(x) = d2/dx2 ln Γ(x), x 0, -1, -2,
POCH
(a)x = Γ(a + x)/ Γ(a), if a + x = 0, -1, -2, then a must = 0, -1, -2,
POCH1
((a)x - 1)/x, if a + x = 0, -1, -2, then a must = 0, -1, -2,
BETA
β(x1, x2) = Γ(x1) Γ(x2)/ Γ(x1 + x2), x1 > 0 and x2 > 0
CBETA
β(z1, z2) = Γ(z1) Γ(z2)/ Γ(z1 + z2), z1 > 0 and z2 > 0
ALBETA
ln β(a, b), a > 0, b > 0
BETAI
Ix(a, b) = βx(a, b)/ β(a, b), 0 x 1, a > 0, b > 0
Published date: 03/19/2020
Last modified date: 03/19/2020