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Saturday, March 14, 2009
Note - the approximation for F(x) = x -x^3/3 + x^5/5 -.... is rapidly convergent for a range of -1< x <1 but inefficiently convergent for values out of that range, however this range of accuracy could be horizontally shifted by setting x. as something other than 0 in the Taylor Polynomial Approximation.
- Or - you could solve this for x>1 by setting F(x)= pi/2 - F( 1/x ),
where pi/2 is the sum sequence derived (2-2/3+2/5-2/7+2/9-....)