<p> Hatch </p>

db904797-ba49-4bcd-94a2-7f0f968c9c2f 20 4 5 decimal

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

Exponential Integral

γ 0.577215664901532860606512 :

http://keisan.casio.com/exec/system/1180573423

x Ei γ x ln + x k^k k! (* / k 140 sum + :

complementary Ei(x) x E1 γ x ln + x - (k^k k! (* / k 140 sum + :

x D x - exp x / :

x Ei x D 2 1 sys

x Ei t - exp t / t x ∞ int ≡

x Ei x - E1 2 1 sys

3 Ei 9.93383257062542

x E1 t - exp t / t x - ∞ int - ≡

<p> Hatch </p>

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) 
between functions f(x) and g(x) in x-range from x1 to x2 f g x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

x f x Ei : x g 0 : 12 mat

U 1.5 : X 3 : 12 mat

Cumulative integration

U Ei X Ei 21 mat 3.30128544912979 9.93383257062542 21 mat

Integral accuracy 10000 => slow x Ei x 13 int 10.5391248008473

x f x 0.3 0.6 solve 0.3725

x Ei f g 0.01 U 10 hatch f g U X 20 hatch 3 1 sys

The complete plot for evaluation x Expi x Ei Re x 0 ≤ x - E1 Re cases :

x Expi

1 - Expi 1 Expi 21 mat 0.219383934395519 - 1.89511781635594 21 mat

CONFLICT: [conflict in coding]
Rmanujan needs a special way to construct
1. call the Σ[n operator] 
2. in the place holder: paste the [n,k]arguments Ramanujan γ 0.577215664901532860606512 : x Li γ x ln ln + x sqrt 1 - (n 1 -^x ln (n^* n! (2 n 1 -^* / 12 k * 1 + / k 0 n 1 - (2 / Floor sum * n 120 sum * + : 31 line

Construct these two terms separately,
then paste in the place holder  Σ[n=1,20] 1 - (n 1 -^x ln (n^* n! (2 n 1 -^* / 12 k * 1 + / k 0 n 1 - (2 / Floor sum *

x Li e 5 e 5 - 2 2 mat 1 5 1 5 - 2 2 mat 3 1 sys

X e :

sanity:  1.89511781635594 X Li 11 mat 1.89511781635594 11 mat