>>>>> "Vickram" == Vickram Ratnam <accts at goldox.mu> writes:
Vickram> I?m trying to compute a definite integral using
Vickram> Woollett?s tanh-sinh maxima code and the maxima built-in
Vickram> integration methods but with no success!
Vickram> My function is the following:
Vickram> 1/sqrt((.0000812*(1+x)^4)+(.2719188*(1+x)^3)+(0*(1+x)^2)+.728)
Vickram> From 0 to 1e+13
Vickram> Using preferably tanh-sinh quadrature and to over 300 digits accuracy!
I don't have a copy of Ted's tanh-sinh method handy, but what's the
point of computing the integral to 300 digits when the numbers appear
to have at most 7 digits of accuracy? If they are supposed to be
exact, make them rationals. And once you do that, the integrand is
1/sqrt(quartic), which mans it's an elliptic integral. Maxima doesn't
have any routines to convert that to the corresponding elliptic
functions, but Abramowitz and Stegun includes algorithms to do that.
And once you have the elliptic functions, maxima can calculate them to
whatever accuracy you want.
Ray