Superfactorial.cin

// superfactorial.cin or superfac.cin is routine for the efficient evaluation of the SuperFactorial of complex argument.

z_type superfac0(z_type z){ int n; z_type s; //     DB K=1.8455686701969342788; DB k=0.61278745233070836381366079016859252; //k=log(K); DB u[21]={2.,1., //0,1 .798731835172434541585621072345730147, // 2 .577880975476483235803807592348110833,  // 3 .393978809662971757177848639852917378,  // 4 .257533958032332679820773329133486586,  // 5 .162901958103705249541496101752195514,  // 6 .100282419171352371943554511785342142,  // 7 .0603184725913977494512136774562415014, // 8 .0355544582258061836048059212969418417, // 9 .0205859954874424134686332481358935023, //10 .0117302279624549548734823541033644211, //11 .00658835541777254650743317221091667507,//12 .00365218351418374834372649788987162842,//13 .00200039479760669665711545138631474960,//14 .00108362752868222808502286098449166985,//15 .000581036636299227699924018045799185045,//16 .000308601963223618214714523083268563975,//17 .000162 ,.000084, 0.000043      //18,19,20 }; z_type e=exp(k*z); s=u[20]; for(n=19;n>=0;n--){s*=e; s+=u[n];} //     s=u[15]; for(n=14;n>=0;n--){s*=e; s+=u[n];} return s;}

z_type superfac(z_type z){ if(Re(z)>-2.)  return fac(superfac(z-1.)); return superfac0(z-0.919385965452180); }

// //