How can we go about finding the Indefinite product integral of polynomials in closed form?
The goal is to some how find the Product integral of a polynomial including the polynomial's constant term. There are some constraint to the input.
- The range the of input polynomial will be greater than 0.001 except for its end behavior.
- The Polynomial is very large, up to $ ax^{512} $
I tried taking the this approach by integrating the natural log of the function and raising $e$ to the output, $ {\displaystyle \lim _{\Delta x\to 0}\prod {f(x_{i})^{\Delta x}}=\exp \left(\int _{0}^{x}\ln f(5x^3+x^2 ...)\,dx\right),} $ but I could not find a closed form solution when there was a constant term.