Sqrt2f23l.cin

// Sqrt2f23l.cin suggests routine F23L for evaluation of real–holomorphic abelexponential to base \(b\!=\!\sqrt{2}\).

//In order to evaluate \(\mathrm{tet}_{\sqrt{2}}(z)\), the routine should be called as F23L(z)

z_type f23L(z_type z){ int n; z_type e,s,k;
DB TcL[23]={1., //coeff. of expansion of exp(-q(z+1.2 ...) by powers of (2-F).
 -.56472283831773236365, 0.29964618138408807683,
 -.15593239048925425850, 0.8035187974815443609e-1,
 -0.411584960662439279e-1, 0.2099852095441203541e-1,
 -0.1068258032026355653e-1, 0.542288102231591005e-2,
 -0.2748252661868267e-2, 0.13909151872677962e-2,
 -0.703181586212482131e-3, 0.35517006776480e-3,
 -0.1792537427481520668e-3, 0.9040887657183e-4,
 -0.45572543028501136e-4, 0.2296022632181e-4,
 -0.1156277075032e-4, 0.5820169657e-5,
        -0.291e-5, 0.144e-5, -.71e-6 };
z=2.-z; s=TcL[22]; for(n=21; n>=0; n--){ s*=z; s+=TcL[n]; }
// return -log(s*z)/0.36651292058166432701 -1.251551478822190;};
        return -log(-s*z)/0.36651292058166432701+2.131917787095039;};
                //.32663425997828098238;

//z_type TQ2L3(z_type z){ DB b=sqrt(2.); if(abs(z-2.)>9999.) return 9999.;
z_type F23L(z_type z){ DB b=sqrt(2.); if(abs(z-2.)>9999.) return 9999.;
                        if(abs(z-2.)>.4) return F23L(exp(z*log(b)))-1. ;
                         return f23L(z); }

/**/