Sqrt2f23e.cin

// Sqrt2f23e.cin suggests routine F21E for evaluation of real–holomorphic superexponential to base \(b\!=\!\sqrt{2}\).

//In order to evaluate \(\mathrm{tet}_{\sqrt{2}}(z)\), the routine should be called as F23E(z)

 z_type f23E(z_type z){int n; z_type e,s; DB coefd[24];
 DB coef[24]= { -1., // 0 (first power coeff)
 0.56472283831773236365, -0.33817758685118329988, // 2
 0.21033130213862776975, -0.13445487905210979672, // 4
 0.087784388601219137357, -0.058288093083094691542, // 6
 0.039240711783727838328, -0.026723286034298143846, // 8
 0.018376520597637595915, -0.012742089846776647861, //10
 0.0088986329515697318595, -0.0062531995639748853846, //12
 0.0044181328624396520598, -0.0031365295362695967035, //14
 0.0022361213774486947923, -0.0016001999145218074082, //16
 0.0011489818761273047343, -0.00082749213843167597835, //18
 0.00059758321720686253893, -0.00043261919624398863166, //20
         0.0003158, -0.00023 , .00017 //last 2 are doubtful.
 };
 e=exp(-0.36651292058166432701*(z-2.131917787095039));
 s=coef[23];
 for(n=22;n>=0;n--) { s*=e; s+=coef[n]; }
 return 2.-s*e;
 }

// z_type TQ2E3(z_type z){ if(Re(z)>5.) return tq2e3(z);
// return log(TQ2E3(z+1.))/log(sqrt(2.)); }
 z_type F23E(z_type z){ if(Re(z)>5.) return f23E(z);
                         return log(F23E(z+1.))/log(sqrt(2.)); }

        // (0,3) superfunction of exp_{sqrt{2}}

/**/