Analuxpf3c.cin

// analuxpf3c.cin is C++ implementation of the elementary function \(\mathrm{Fit}_3\) and related functions, that provides approximation of natural tetration for moderate values of the argument.

// This fit had been used to guess the asymptotic behaviour of tetration at \(\mathrm i \infty\).

// z_type should be defined as complex

// In order to evaluate the approximation at artument \(z\), type  F3(z) 

//

z_type s2(z_type x){ return exp(exp(x-2.51))-.6+.08*(x+1.); } z_type f1(z_type x){ return log(x+2.) + exp(x-1.);} z_type f2(z_type x){ return log(2.+x) + (1.+x)*(       1. + .5*exp((x-1.)*s2(x))*x*(M_E-2.+log(4./3.)) - log(2.)         );} z_type f3(z_type x){ return .6*f2(x)+.4*log(f2(x+1.)) ;} z_type F3(z_type z){ DB x=Re(z); if(x<-1) return log(F3(z+1.)); if(x>0) return exp(F3(z-1.)); return f3(z); } z_type F2(z_type z){ DB x=Re(z); if(x<-1) return log(F2(z+1.)); if(x>0) return exp(F2(z-1.)); return f2(z); } z_type F1(z_type z){ DB x=Re(z); if(x<-1) return log(F1(z+1.)); if(x>0) return exp(F1(z-1.)); return f1(z); }