Interpolation by rational functions

Please choose:

My own (x,y) -data
Numerator degree l= Important: 0 <= n <= 40 !
Denominator degree m= Important: 0 <= m <= 40 !

Important: 0 <= l+m <= 40 !!!

Please write your l+m+1 (x,y) data here, x and y separated by blank or comma, no parentheses, each pair on a new line

(x,y)=
Synthetic data

Choose a function:
f(x) = tan(x π /2)
f(x) = 1/(1+25x2)
f(x) = (x**2)**(1/3)
f(x) = tanh(x)
f(x) = exp(x)
Input of a self defined function:
Please type the evaluation program of your function here using FORTRAN rules. Your final statement must be
      fu=
You may use the constants pi, e(=exp(1)), sqrt2(=1.414...), the integer variables i,j,k, the logicals bool1,bool2,bool3 and the double precision variables sum,h1,h2,h3,h4,y(100),z(100),a(100,100) which are all intialized with zero resp. .false. . The routine has the parameters x (double, input) and fu (double out). never change x!. first is a local integer and set 0 before calling the function the first time. You may use this in order to initialize some local data and set it 1 afterwards to avoid multiple such initialization. Your settings of the local variables are preserved during program execution.

Please specify the degrees here:
Numerator degree l= Important: 0 <= l <= 40 !
Denominator degree m= Important: 0 <= m <= 40 !

Important: 0 <= l+m <= 40 !!!

Please specify the interval for the x-data [a,b]
a = b =

How should the x-data be distributed ?
equidistant (hence x(i)=a+(b-a)*i/(l+m) )
transformed Chebyshev abscissae
(hence (a+b)/2+(b-a)/2*cos((2i+1)π/(2(l+m+1))) )

Click on "evaluate", in order to submit your input.

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27.09.2018