/usr/share/openturns/validation/Debye.txt is in openturns-validation 1.5-7build2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 | > restart:
> solve(t/(t+2)=y,t);
2 y
- ------
-1 + y
> help(Debye);
Error, Could not find any help on "Debye"
> solve(int(u/(exp(u)-1),u=0..x)/x=y,x);
2 2
ln(-exp(RootOf(-6 _Z ln(-exp(_Z) + 1) + Pi + 3 ln(-exp(_Z) + 1)
- 6 polylog(2, -exp(_Z) + 1) + 6 y ln(-exp(_Z) + 1))) + 1)
> debye:=Int(u/(exp(u)-1),u=0..x)/x:
> eval(debye);
> pol:=convert(series(debye,x=4,20),polynom):
x
/
| u
1/x | ---------- du
| exp(u) - 1
/
0
> plot(log(abs(pol-debye)),x=0..15);
Warning, computation interrupted
> plot(debye-pol,x=0..5);
> allvalues(solve(value(debye)=y,x));
ln(-exp(RootOf(6 _Z ln(-exp(_Z) + 1) + 6 polylog(2, -exp(_Z) + 1)
2 2
- 6 ln(-exp(_Z) + 1) - Pi - 3 ln(-exp(_Z) + 1)
2
+ 6 y ln(-exp(_Z) + 1) )) + 1)
> plot(1-4*(1-debye)/x,x=-5..5);
> series(1-4*(1-debye)/x,x);
3 4
1/9 x - 1/900 x + O(x )
> Digits:=30;fsolve((x/9-x^3/900)/(1-4*(1-value(debye))/x)-1=-1e-16,x);
Digits := 30
-0.000875677785080733459909609107099
> plot((abs((x/9-x^3/900)/(1-4*(1-value(debye))/x)-1)),x=-0.001..0.001);
> k:=2:limit(int(t^k/(exp(t)-1),t=0..x)/x^k*k,x=0,left);
1
> expand(factor(n/x^n*x^n*(1/n-x/(2*(n+1)))));
n 1 x n
----- + ----- - ---------
n + 1 n + 1 2 (n + 1)
>
|