Terse Schroeder & Abel function code Daniel Fellow   Posts: 248 Threads: 80 Joined: Aug 2007 10/02/2022, 02:42 PM (This post was last modified: 10/02/2022, 02:43 PM by Daniel.) The following provides the Schroeder and Abel functions in Mathematica using the support for solving recursive equations and Bell polynomials. The code takes about a hour to run for the first ten derivatives. Code:order=10; H=0; H=f'^t ; Do[H[max]=First[r[t]/.RSolve[{r==0,r[t]==Sum[Derivative[k][f]BellY[max,k,Table[H[j]/.t->t-1,{j,max}]],{k,2,max}]+ f' r[t-1]},r[t],t]],{max,2,order}]; Schroeder=f'^t z+Sum[1/k! H[k]z^k,{k,2,order}] Abel=Limit[Schroeder,{f'->1}] Daniel Daniel Fellow   Posts: 248 Threads: 80 Joined: Aug 2007 10/16/2022, 07:03 AM The Pari/GP code for Bell polynomials is Code:  Bell(k,n=-1)=   { my(x, v, dv, var = i->eval(Str("X",i)));       v = vector(k, i, if (i==1, 'E, var(i-1)));     dv = vector(k, i, if (i==1, 'X*var(1)*'E, var(i)));     x = diffop('E,v,dv,k) / 'E;     if (n < 0, subst(x,'X,1), polcoef(x,n,'X));   } So to Mathematica code at the beginning of this thread can be migrated to Pari/GP. Daniel « Next Oldest | Next Newest »

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