static ScalarValue DiLog1(ScalarValue e)
{
ScalarValue f = new ScalarValue(Math.PI * Math.PI / 6.0);
if (e == 0.0)
{
return(f);
}
var L = e.Ln();
var ek = ScalarValue.One;
for (int k = 1; k < 250; k++)
{
var f_old = f.Clone();
ek *= e;
var df = ek * (L - 1.0 / k) / k;
f += df;
if (f == f_old)
{
return(f);
}
}
throw new YAMPNotConvergedException("spence");
}
static ScalarValue LogGamma_Stirling(ScalarValue z)
{
if (z.Im < 0.0)
{
return(LogGamma_Stirling(z.Conjugate()).Conjugate());
}
var f = (z - 0.5) * z.Ln() - z + Math.Log(2.0 * Math.PI) / 2.0;
var reduce = f.Im / (2.0 * Math.PI);
reduce = f.Im - (int)(reduce) * 2.0 * Math.PI;
f = new ScalarValue(f.Re, reduce);
var zsqu = z * z;
var zp = z.Clone();
for (var i = 1; i < 10; i++)
{
var f_old = f.Clone();
f += Helpers.BernoulliNumbers[i] / (2 * i) / (2 * i - 1) / zp;
if (f == f_old)
{
return(f);
}
zp = zp * zsqu;
}
throw new YAMPNotConvergedException("gamma");
}
static ScalarValue DiLog0(ScalarValue z)
{
var zz = z.Clone();
var f = zz.Clone();
for (int k = 2; k < 250; k++)
{
var f_old = f.Clone();
zz *= z;
f += zz / (k * k);
if (f == f_old)
{
return(f);
}
}
throw new YAMPNotConvergedException("spence");
}
static ScalarValue DiLog0(ScalarValue z)
{
var zz = z.Clone();
var f = zz.Clone();
for (var k = 2; k < 250; k++)
{
var f_old = f.Clone();
zz *= z;
f += zz / (k * k);
if (f == f_old)
{
return f;
}
}
throw new YAMPNotConvergedException("spence");
}
static ScalarValue LogGamma_Stirling(ScalarValue z)
{
if (z.Im < 0.0)
{
return LogGamma_Stirling(z.Conjugate()).Conjugate();
}
var f = (z - 0.5) * z.Ln() - z + Math.Log(2.0 * Math.PI) / 2.0;
var reduce = f.Im / (2.0 * Math.PI);
reduce = f.Im - (int)(reduce) * 2.0 * Math.PI;
f = new ScalarValue(f.Re, reduce);
var zsqu = z * z;
var zp = z.Clone();
for (var i = 1; i < 10; i++)
{
var f_old = f.Clone();
f += Helpers.BernoulliNumbers[i] / (2 * i) / (2 * i - 1) / zp;
if (f == f_old)
{
return (f);
}
zp = zp * zsqu;
}
throw new YAMPNotConvergedException("gamma");
}
static ScalarValue DiLog1(ScalarValue e)
{
var f = new ScalarValue(Math.PI * Math.PI / 6.0);
if (e == 0.0)
{
return f;
}
var L = e.Ln();
var ek = ScalarValue.One;
for (var k = 1; k < 250; k++)
{
var f_old = f.Clone();
ek *= e;
var df = ek * (L - 1.0 / k) / k;
f += df;
if (f == f_old)
{
return f;
}
}
throw new YAMPNotConvergedException("spence");
}