50d40ed8-9113-4352-8776-a862092e527d 23 4 5 decimal

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

"eval(■ )" ... solves & assigns in-situ X x erf vectorize 1 x / - 0 ≡ x 1.5 - 1.5 solve eval : 1.1255 - 1.1255 21 mat

4 appVersion 0.98.6179.21440 ≡

x erf 1 x / 2 1 sys

x y axes x y / - :

x erf vectorize

x q x :

The MYSTIC plots: 1. erf(x) rejects other plot(s), except "axes" 2. erf(x) plots only if 'x' is ranged above ! 3. plots the "entire" erfc(x,n) 4. rejects q(x) ? ? ?

x 1.5 - 5 1.49 - range :

x erf axes x 2 erfc x q 4 1 sys

a 0.5 : b 1 : xn b a + (2 / : 31 line

x f x erf x q - eval :

ε 1010 -^:

Dichotomy 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 31 line

sanity

xn 0.617446879

xn f 41011 -^*

n 27

x erf x q x 2 erfc 3 1 sys

has NO indefine/definite integral representation
has various approximations for CAS systems.
∫f(x)≡erf(x) as explicited Mathcad 11. x f 2 π sqrt / x 2^- exp * :

x Clear 1

Revisit erf(x) ... erfc(x)

x erf 2 π sqrt / t 2^- exp t 0 x int * ≡

must be vectorized
acc 2000  1.436788439167190
exact =>  1.436788439167195 x erf vectorize x 02 int 1.436788439308650

1rst derivative ...
is simply the integrand x D 2 π sqrt / x 2^- exp * :

Typical Hysterisis representation

x erf x 0.5 erf 2 1 sys

n 2 :

x Clear 1

'n' derivative x D x n diff 4 x 2^- exp * 12 x 2^* - (* π sqrt / -

constrain the plot ["] x u 12 - x ≤ (x 2 ≤ (& cases :

x erf x D x D x 1 diff x D x 2 diff 0.5 x D x 3 diff * 5 1 sys x 1 erfc x 2 erfc x 3 erfc x 4 erfc x 3 erf 6 1 sys

x f x erf vectorize 2 π sqrt / x 2^- exp * 4 x * x 2^- exp * π sqrt / - 4 x 2^- exp * 12 x 2^* - (* π sqrt / - 8 x * x 2^- exp * 32 x 2^* - (* π sqrt / 51 sys :

Vectorize erf(x) ... QuickPlot

x f

Observatory cumulative integration ... I have found NO other setup of that style.

x f 2 π sqrt / x 2^- exp * :

ε ≥ 10^{-8} ε 108 -^:

Observatory Ox 1.9 - ε + (:

Σ U 2 - 3.1 Ox range : j 1 U rows range Cumul j el x f x U 1 el U j el int : for U Cumul augment 31 line :

Σ Σ eval :

Σ x f x erf vectorize 3 1 sys

Σ Σ rows row 3 1.9953 12 mat

3 erf 1

u 0.5 - :

u erfc 1 u erf - 21 mat 1.5205 1.5205 21 mat

Disambiguate erfc(x):=1-erf(x,■)

Why ... incomplete plots ?

x erfc x 1 erfc x 2 erfc 3 1 sys

Complete plots version

1 x erf - 1 x 1 erf - 1 x 1.5 erf - 3 1 sys 1 xx erf vectorize -