55d6afaa-f99e-44e5-905d-9505d3662628 3 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

"RootSecant" intersect ... descending ▼ convergents Φ a b ε X u 1 el ε : u 2 el b b Φ a b - (* a Φ b Φ - / - : i 2 : u i 1 + el u i el u i el Φ u i 1 - el u i el - (* u i 1 - el Φ u i el Φ - / - : u i el u i 1 - el - abs ε > u i 1 + el u i el u i el Φ u i 1 - el u i el - (* u i 1 - el Φ u i el Φ - / - : i i 1 + : 21 line while u 61 line :

Solve(f,q,x0,x1,TOL) ... The core component is solve(4) If the funct is not scalar wrt 'x' ... Gamma(x)is NOT. ... solve(4) & roots(3) fail Alternately RootSecant X(Φ,a,b,ε) Bracket X(Φ,■,■,ε) for last 2 convergents =

x Γ x Gamma :

N n p x hypergeom N 1 + Γ n 1 + Γ * N n + p - 1 + Γ * p 1 + Γ * x 1 + Γ x - n + 1 + Γ * N n + 1 + Γ * x N + p - 1 + Γ * x - p + 1 + Γ * / :

N 39 :

n 12 :

p 20 :

ε 1015 -^:

x hypergeom N n p x hypergeom :

x f 0.025 x * :

x Φ x hypergeom x f - eval :

parametric command line X Φ 6 6.5 ε X :

u X X rows el : 6.23315640883423

parametric command line XX Φ 1.875 2.125 ε X :

x hypergeom x f u u f + 20 black 1 5 mat 3 1 sys

X 11015 -^* 6.23410483488073 5.48475611649919 6.23309978239644 6.23315979534205 6.23315640883647 6.23315640883415 6.23315640883435 6.23315640883422 6.23315640883423 6.23315640883423 111 mat

XX 11015 -^* 1.91803450244985 1.50167071402424 1.9271166225024 1.92331993346546 1.9244324203465 1.92443455823882 1.92443455653425 1.92443455653433 1.92443455653431 1.92443455653431 111 mat

Bracket wisely for the last 2 convergents =