Elliptic integrals

[salvomic]

(11-03-2017 01:54 PM)AlexFekken Wrote:  In the first pair of calculations you are integrating over a singularity at the end of the integration internval when you use the non-trig defiinition (i.e. at x=t=1). The trig version does not have that singularity. So I suspect that the integration algorithm gives you a less accurate result because of that singularity, i.e. it is not so good at guessing the limit of the improper Riemann integral.

This seems to be comfirmed by the second pair of calculations where you are staying away from the singularity and the results are essentially the same.

thank you for the explaining, Alex.
Yes, I left the first pair in non trig definition for studying purpose, as they are well know in this form, however you are right: so there is a singularity to avoid (and in effect the Prime gives also a message first to calculate). Surely the code could be stronger, but I'd not want to pass at trig-form for the 1st pair, for now...


Salvo