E1etf.cin

// e1etf.cin is routine that evaluates tetration to Henryk base \(\eta=\exp(1/\mathrm e)\). // z_type e1etf(z_type z){ int n,N; z_type c,f; z+=2.798248154231454; z_type t=log(z); z_type u=-1./(3.*z); z_type s[16]; s[0]=                    1.; s[1]=                    t; s[2]=                  t*(t-  1.   )+  .5; s[3]=              t*(t*(t-  5/ 2.)+   5/ 2.)-   7/10.; s[4]=           t*(t*(t*(t- 13/ 3.)+  45/ 6.)-  53/10.)+   67/60.; s[5]=        t*(t*(t*(t*(t- 77/12.)+ 101/ 6.)-  83/ 4.)+  653/60.)- 2701/1680.; // this seem s[6]=     t*(t*(t*(t*(t*(t- 87/10.)+  95/ 3.)- 175/ 3.)+  267/ 5.)-17245/ 840.)+   92461/42000.; s[7]=  t*(t*(t*(t*(t*(t*(t-223/20.)+1591/30.)- 535/ 4.)+ 5488/30.)-30061/ 240.)+  503159/14000.)-348617/84000.; s[8]=t*(t*(t*(t*(t*(t*(t*(t-481/35.)+2947/36.)-8011/30.)+29977/60.)- 9305/ 18.)+11298583/42000.)-580789/8400.)+4558331/352800.; s[9]= t*(t*(t*(t*(t*(t*(t*(t*(t-4609/280.)+16659/140.)-43417/90.)+349903/300.)-199529/120.)+166822247./126000.) -48732671./84000.)+21806039./117600.)-12523881847./388080000.; N=9; c=s[N]*u; for(n=N-1;n>0;n-=1){c+=s[n];c*=u;}  c+=1.; return M_E*(1.-(2./z)*c); }

z_type E1ETF(z_type z){ if(Re(z)>12)    return e1etf(z); if(fabs(Im(z))<5.)return log(E1ETF(z+1.))*M_E; if(abs(z-3.)<16)  return log(E1ETF(z+1.))*M_E; return e1etf(z); } //