tpfto / carlson Goto Github PK

One reason for writing a package for the Carlson functions was to facilitate the derivation of elliptic integral expressions. To that regard, I plan to combine the information in Carlson's series of papers to reduce any elliptic integral to his set of standard functions with the implementation in Rubi, so that one can get elliptic integral expressions that are not needlessly complicated. (By contrast, current symbolic results for elliptic integrals in Mathematica often have unneeded complex factors, even when the results should be real.)

This part of the project is quite nontrivial, and might take a while longer to implement properly.

Some other planned symbolic functionality I hope to implement in the near future include the following:

1. Interconversion between Carlson integrals and the Legendre-Jacobi integrals (EllipticF[], EllipticE[], ElllipticPi[], EllipticK[]).

2. Further calculus support (integration of elliptic integrals, limits, series expansions, etc.)

3. Implement simplification identities with functions already in Mathematica (e.g. elliptic functions, theta functions) for FunctionExpand[]/FullSimplify[].

Other suggestions for added symbolic functionality are welcome.