| public static ChebEval ( ChebSeries cs, Double x ) : Double | ||
| cs | ChebSeries | The coefficients to consider. |
| x | Double | The real evaluation argument. |
| return | Double | |
static double RiemannZeta1msLt0(double s)
{
if (s > -19.0)
{
var x = (-19 - 2.0 * s) / 19.0;
var c = Helpers.ChebEval(zetaGt1, x);
return(c / (-s));
}
var f2 = 1.0 - Math.Pow(2.0, -(1.0 - s));
var f3 = 1.0 - Math.Pow(3.0, -(1.0 - s));
var f5 = 1.0 - Math.Pow(5.0, -(1.0 - s));
var f7 = 1.0 - Math.Pow(7.0, -(1.0 - s));
return(1.0 / (f2 * f3 * f5 * f7));
}
static ScalarValue RiemannZeta1msLt0(ScalarValue s)
{
if (s.Re > -19.0)
{
var x = (-19 - 2.0 * s) / 19.0;
var c = Helpers.ChebEval(zetaGt1, x);
return(c / (-s));
}
var f2 = 1.0 - new ScalarValue(2.0).Pow(-(1.0 - s));
var f3 = 1.0 - new ScalarValue(3.0).Pow(-(1.0 - s));
var f5 = 1.0 - new ScalarValue(5.0).Pow(-(1.0 - s));
var f7 = 1.0 - new ScalarValue(7.0).Pow(-(1.0 - s));
return(1.0 / (f2 * f3 * f5 * f7));
}
static double RiemannZetaGt0(double s)
{
if (s < 1.0)
{
var c = Helpers.ChebEval(zetaLt1, 2.0 * s - 1.0);
return(c / (s - 1.0));
}
else if (s <= 20.0)
{
var x = (2.0 * s - 21.0) / 19.0;
var c = Helpers.ChebEval(zetaGt1, x);
return(c / (s - 1.0));
}
var f2 = 1.0 - Math.Pow(2.0, -s);
var f3 = 1.0 - Math.Pow(3.0, -s);
var f5 = 1.0 - Math.Pow(5.0, -s);
var f7 = 1.0 - Math.Pow(7.0, -s);
return(1.0 / (f2 * f3 * f5 * f7));
}
static ScalarValue RiemannZetaGt0(ScalarValue s)
{
if (s.Re < 1.0)
{
var c = Helpers.ChebEval(zetaLt1, 2.0 * s - 1.0);
return(c / (s - 1.0));
}
else if (s.Re <= 20.0)
{
var x = (2.0 * s - 21.0) / 19.0;
var c = Helpers.ChebEval(zetaGt1, x);
return(c / (s - 1.0));
}
var f2 = 1.0 - new ScalarValue(2.0).Pow(-s);
var f3 = 1.0 - new ScalarValue(3.0).Pow(-s);
var f5 = 1.0 - new ScalarValue(5.0).Pow(-s);
var f7 = 1.0 - new ScalarValue(7.0).Pow(-s);
return(1.0 / (f2 * f3 * f5 * f7));
}