(i^2+i*alpha+i*beta+i)*Q(n)+((-x*alpha-x*beta-2*x+beta-alpha)*n-x*alpha-x*beta-2*x+beta-alpha)*Q(n+1)+((1-x^2)*n^2+(-3*x^2+3)*n-2*x^2+2)*Q(n+2) = 0

After using diffeqtorec, there is n in coefficient, if multiply x^n/n! to all terms, i can not convert some to exponential function due to n^2, n and the difference of outer coefficient n not greater than n+2 in Q(n+2)

as i do not know the initial condition of above formula, differential equation is no use.

Is there a command to change differential equation into difference equation?

Any command convert any polynomial to generating function, Any general method?

such as summation f(n)*x^n/n! where f(n) may have recurrence relation

how to use reduce command to get prime ideal?

i find PrimeDecomposition and PrimaryDecomposition in package with(polynomialideal):

is the primedecomposition for prime ideal?

any command same as http://www.singular.uni-kl.de/Manual/3-0-4/sing_244.htm