7482edb2-290d-4dfa-94fd-032d2ba9eb14 55 3 5 decimal

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

Read 1rst ...

x β f x x β 3 el x * β 2 el + β 4 el x 2^* + (* β 1 el + (* 1 x x β 7 el x * β 6 el + β 8 el x 2^* + (* β 5 el + (* + / :

fuck it ! erf x erf x diff #

Transit the derivative opertor x β Deriv x β f (x diff :

β 4.69292878185 2.485645088668 0.005049502793 - 0.008399478307 - 5.19337552684 0.698811411628 0.043875966805 - 0.000673223801 - 81 mat :

x β βDeriv x β Deriv 0 x ≤ (x 15 ≤ (& OUT range cases :

0 β βDeriv 4.692929

x β Φ x β f 0 x ≤ (x 15 ≤ (& OUT range cases :

x β βDeriv x β Φ 0 4.693 . 15 red 1 5 mat 3 1 sys

... read next => "Finite Differences [Fnct, Deriv, Cumul].sm"

f L H N Project Discretise the function dx H L - N / : i 1 N range U i el L dx - (dx i * + : for i 1 U rows range vx i el U i el : vy i el U i el (f : 21 line for vx vy augment 51 line :

[L,H] range Npts L 5 - : H 5 : N 200 : h H L - N / : 14 mat 11 sys

x f 11 x 2^+ / :

<= Sanity check function

x h D1 x 2 h * + f - 8 x h - f * + 8 x h - f * - x 2 h * - f + 12 h * (- / :

x h D2 x 2 h * + f - 16 x h + f * + 30 x f * - 16 x h - f * + x 2 h * - f - 12 h 2^* / :

n 3 :

x f x n diff x f x 4 diff 2 1 sys x f x h D1 x h D2 3 1 sys

Work erf(x) wisely !

x D1 2 π sqrt / e x 2^-^* :

x erf x diff 2 π sqrt / e x 2^-^* ≡

n x Dn x D1 x n diff :

n 1 :

m 2 :

a 8 π 3 - (* 3 π * 4 π - (* / : 0.140012

Approximation erf(x)

x erf x D1 n x Dn m x Dn 4 1 sys

x erf x sign 1 x 2^4 π / a x 2^* + 1 a x 2^* + / (* - exp - sqrt * :

0 x erf 2 1 sys x erf x diff

# 1rst Deriv 2nd Deriv m Deriv 31 mat ≡