I want to calculate the following formula:
but I can’t find the integrator module as Int() in MATLAB.
how could I solve the problem using Julia?
Use QuadGK.jl
3 Likes
This particular integral can be done analytically. The answer is:
\sum_{i=0}^{10} \frac{N!}{i! (N-i)!} \frac{1}{\lambda (N-i) (N-i+1)}
or, in Julia:
f(λ,N) = sum(binomial(N,i) / (λ*(N-i)*(N-i+1)) for i = 0:10)
assuming N > 10.
26 Likes
As far as I can see int() is the function to do symbolic integration in matlab. In fact matlab contains nowadays a complete computer algebra system (CAS) as part of some toolbox (it is in fact the old MUPAD).
In julia there appears to be a package to use either SymPy or Reduce directly. Both are quite capable systems. I have not tested if they can solve that integral. But maxima (another free CAS, but without a working julia interface) can, so it should be ok.
3 Likes