RE: Capacitance of horned torus

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Original poster: "Godfrey Loudner" <ggreen-at-gwtc-dot-net> 



Hello Antonio

I forgot to add a curious formula to my last post.
With some function theory, one can give another
expression for the integral.

Integrate[E^(-a(n)Sinh[t]),{t,0,Infinity}] =

a(n)^(-1) BesselJ[1,a(n)]^(-1) times

[-1 + Integrate[BesselJ[0,t], {t, 0, a(n)}].

Note that a(n) must be a zero of BesselJ[0,x].

This does not help here. I'm told by Mathematica
that my 4.1 version of Mathematica has a bug that's
particular to the numerical approximation of
Integrate[BesselJ[0,x],{x,0,r}]. I guess most
programs have bugs.

Godfrey Loudner