b092a039-dcd7-4b1e-af3c-9bf3822f9dd2 64 3 5 decimal

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n k combin n! k! (n k - (! (* / :

combin(n,k) Returns the number of subsets each of size 'k' that can be formed from 'n' objects, where 'n' is greater or equal to 'k'. Each subset is known as a combination. 'n' & 'k' are integers greater than or equal to zero.

x Γ Gilberto E. Urroz x Γ x Gamma : x 0 ≥ x Γ π x abs 1 + (* x abs 2 + Γ π x abs 1 + (* sin * / if 31 line :

103 combin 120

Vectorise piecewise each Γ(x,") component ... whichever way => does NOT derive ! x N n p hypergeom N 1 + Γ n 1 + Γ * N n + p - 1 + Γ * p 1 + Γ * x 1 + Γ vectorize x - n + 1 + Γ vectorize * N n + 1 + Γ * x N + p - 1 + Γ vectorize * x - p + 1 + Γ vectorize * / :

N 50 :

n 15 :

p 10 :

Continuous PDF Hypergeometric

x N n p hypergeom x 50 15 15 hypergeom x 30 15 10 hypergeom 3 1 sys

Γ(x) ... convenient approximation

x Γ 1 2 1 sys

x N n p hypergeom x 05 int 0.96

x Γ vectorize x 0.5 2.5 int 2.132733

Rescue from infinitesimal analysis

x Φ x Γ 0.25 x ≤ undefined cases :

x f x N n p hypergeom 1 - x ≤ undefined cases :

h 0.0001 : x h Φ Deriv x 2 h * - Φ x 2 h * + Φ - 4 h * / - : 21 line

h 0.00001 : x h f D1 x 2 h * - f x 2 h * + f - 4 h * / - : 21 line

x q 0 :

ε 103 -^:

x u 1 0.45 x ≤ (x 4 ≤ (* cases :

b 2.5 : a 2 : 12 mat

x F x h f D1 x q - vectorize :

RootDichotomy xn b a + (2 / : n 0 : xn F abs ε > xn F a F * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while xn 51 line

xn 2.117

Derivative Γ(x)

x h Φ Deriv x u *

Deriv => hypergeometric(x,N,n,p)

x h f D1 xn 0 + 20 red 1 5 mat 2 1 sys