public static double SiApprox(double x)
{
return Integrator.Simpsons(t => Math.Sin(t) / t, 1e-8, x, 1 << 10);
// 24/12/2015: The following comment refers to a time when this code belonged
// to an old version of Artemis. Currently, there is no class named UpperSITransition,
// thus the commment is moot. However, the issue involving convergence still persists.
// 7/6/2015: This approximation isn't convergent enough on x > 4π
// to be used by UpperSITransition. The above statement works, but
// is seriously inefficient. Consider implementing something from
// the Cephes library later on.
/*
var x2 = x * x;
// This is the Padé Approximant of Si, given by
// https://en.wikipedia.org/wiki/Trigonometric_integral
return x*(1.0
+ x2*(-4.54393409816329991e-2
+ x2*(1.15457225751016682e-3
+ x2*(-1.41018536821330254e-5
+ x2*(9.43280809438713025e-8
+ x2*(-3.53201978997168357e-10
+ x2*(7.08240282274875911e-13
+ x2*(-6.05338212010422477e-16))))))))
/ (1.0
+ x2*(1.01162145739225565e-2
+ x2*(4.99175116169755106e-5
+ x2*(1.55654986308745614e-7
+ x2*(3.28067571055789734e-10
+ x2*(4.5049097575386581e-13
+ x2*(3.21107051193712168e-16)))))));
*/
}
