Tet2f4c.cin

Tet2f4c.cin is the C++ routine to evaluate tetration $$\mathrm {tet} _{2}$ of complex argument.

The algorithm is described at

// in order to use it, files GLxw2048.inc and tet2f2048.inc should be also loaded.

The code below copypasted from TORI, http://mizugadro.mydns.jp/t/index.php/Tet2f4c.cin

Code

z_type Zo=z_type( 0.824678546142074, 1.567432123849648); z_type Zc=z_type( 0.824678546142074,-1.567432123849648); DB L=log(2.);// 0.693147180559945 z_type Q=z_type( 0.205110688544989, 1.086461157365470);// =L*Zo+log(L) z_type T=z_type( 5.584142435543391, 1.054218360336937); #include "GLxw2048.inc" z_type f4(z_type z){ /*NOT SHIFTED FOR x1 */ #include"tet2f2048.inc" int j,k,m,n; DB x,y, u, t; z_type c,d, cu,cd; z_type E[2048],G[2048]; DO(k,K){c=F[k];E[k]=log(c)/L;G[k]=exp(c*L);} c=0.; DO(k,K){t=A*GLx[k]; c+= GLw[k]*( G[k]/(z_type( 1.,t)-z) - E[k]/(z_type(-1.,t)-z) );} cu=.5-I/(2.*M_PI)*log( (z_type(1.,-A)+z)/(z_type(1., A)-z) ); cd=.5-I/(2.*M_PI)*log( (z_type(1.,-A)-z)/(z_type(1., A)+z) ); return c*(A/(2.*M_PI)) +Zo*cu+Zc*cd; } DB x1= 0.0262474248816494; z_type F4(z_type z){ DB x=Re(z); if(x<-.5) return log(F4(z+1.))/L; if(x> .5) return exp(F4(z-1.)*L); return f4(z+x1); } //

Keywords

Tetration, Suprfunction, TORI, Cauchi integral Cateogry:Book