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 | *(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 |