Thank you very much for your reaction. I give some more details. I'm working on a technical problem (fluid dynamics) using MAPLE which is going fine. The results are in terms of the in MAPLE defined internal procedures for the Elliptical integrals E(z,k) and F(z,k) with no restrictions on (k,z). In my case z has values in (0,infinity) and k in (0,1). The MAPLE functions are working fine and are, very important, fast. Since I have to program the final result in FORTRAN I looked in the literature on FORTRAN programming to find something on this subject (Numerical Recipes, NAG, etc). The only thing I found were programs with a fixed or limited upper integration limit (z is infinity or a value in (0,1) ). But programs with an variable value of the upper integration limit in (0,infinity) I have not found so far. Therefore, I tried to find the source code of the MAPLE programs of E(z,k) and F(z,k) in order to try to convert them in FORTRAN with the 'CodeGeneration' option of MAPLE. It's all perhaps not very elegant and not very professional but I'm not an expert in this field and all I need is the FORTRAN version of the standard MAPLE procedures E(z,k) and F(z,k) where in my case z is in (0,infinity) and k in (0,1) which should be just as fast as the MAPLE versions. Perhaps somebody can help me.