Help:=proc(): print(`NoLIFexp(PHI,z,N), NoLIF(PHI,z,N), LIF(PHI,z,N)`): end: #The first N terms of the solution of #u(t)=t*PHI(u(t)) #multiplied by n! NoLIFexp:=proc(PHI,z,N) local B,n,t: B:=t: for n from 1 to N+1 do B:=t*subs(z=B,PHI): B:=taylor(B,t=0,n+1): B:=add(coeff(B,t,i)*t^i,i=1..n): od: [seq(coeff(B,t,i)*i!,i=1..N)]: end: #The first N terms of the solution of #u(t)=t*PHI(u(t)) #multiplied by n! NoLIF:=proc(PHI,z,N) local B,n,t: B:=t: for n from 1 to N+1 do B:=t*subs(z=B,PHI): B:=taylor(B,t=0,n+1): B:=add(coeff(B,t,i)*t^i,i=1..n): od: [seq(coeff(B,t,i),i=1..N)]: end: LIF1:=proc(PHI,z,n): coeff(taylor(PHI^n,z=0,n),z,n-1)/n: end: LIF:=proc(PHI,z,N) local n: [seq(LIF1(PHI,z,n),n=1..N)]: end: