e4e9a7b0-b586-4db4-bcf5-5e1ecaeb8089 22 4 5 decimal

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

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 * :

x erf x 1 erf 2 1 sys

n 2 :

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

erfc(x,n)is an entire fnct,
does not plot "entirely". 0.25 - 1 erfc 1.9229

__The recalcitrant solve bloc__

does not assign in-situ but saves sol x erf vectorize 1 x / - 0 ≡ x 1 1.3 solve : #

sol 1.1255

x erf vectorize 1 x / - 0 ≡ x 1 1.3 solve 1.1255

solves & assign in-situ sol x erf vectorize 1 x / - 0 ≡ x 1 1.3 solve eval : 1.1255

x y axes x y / - :

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)

x 1.5 - 1.5 1.49 - range :

x q x erf axes 3 1 sys

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

xx f xx erf xx 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

Antiderivative,
integral curve. z Erf z z erf * z 2^- exp π sqrt / + :

0 Erf 1 π sqrt / ≡

x Erf x 0 0 Erf + 30 red 1 5 mat 3 1 sys

Cumulative integration between limits a 0 : b 2 : 12 mat a b Σ b Erf a Erf - : 21 line

a b Σ 1.43678843916719

option: integral accuracy 10000 x erf vectorize x a b int 1.43678843930865

x y axes x y / - :

X_Y erfc(x,n) plot

x 1.5 - 2 1.49 - range :

x erf axes x 1 erfc x 0.5 erfc 4 1 sys x 1 erfc x 2 erfc x 3 erfc x 4 erfc x 3 erf 5 1 sys

erfc(x,n)is an entire fnct,
does not plot "entirely". 0.25 - 0.5 erfc 1.7112

z erfc 1 z erf - :

x λ 1 1.125 x ≤ (x 2.5 ≤ (& cases :

x 2 erfc x λ * 1 x 2 erf - x erfc 3 1 sys

Disambiguate ...

ζ 0.5 :

erfc(x,n)is an entire fnct,
does not plot "entirely". 0.5 - 1 erfc 1.9661

Smath style 0 ζ erfc 1.52049987781305

Mathcad style 0 ζ - erfc 1.52049987781305

Erfc x 2 - 4 1.95 - range : j 1 x rows range E j el x j el ζ erfc eval : for x E augment 31 line :

similar plot Mathcad erfc(x-ζ)

Erfc 0 0 ζ erfc + 20 blue 1 5 mat 3 1 sys

Smath default incomplete plot

x ζ erfc 0 0 ζ erfc + 20 red 1 5 mat 2 1 sys

0 ζ erfc 0 ζ - erfc ≡