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}}

/*