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, x ≠ 0, -1, -2, …
ALGAMS                  ln ǀΓ(x)ǀ and sign Γ(x), x ≠ 0, -1, -2, …
GAMI                      
GAMIC                   
GAMIT                    γ*(a, x) = (x⁻1a/ Γ(a))γ(a, x), x ≥ 0
PSI                                         ψ(x) = Γ´(x)/ 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

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