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### indicial equation

Let N be an integer. Let a, b, A_1,...,A_N be constant real numbers. Let g(n) be a real function of integer variable n.

g(n) satisfies the recurrence equation:

(n + 1)(n + b)g(n+1) = (n + a)g(n) + sum(i=1 to N)(A_ig(n-i))

with g(n)=0 for n<0 . g(0) is obtained through boundary conditions, so it can be considered a given constant.

I need to know the general functional form of the term g(n), as a function of the given constants of the problem: a,b,N,A_1,...,A_N and g(0).

Could you help me? I could I programm in SAGE the code to provide the searched general term g(n)?

Javier Garcia

### indicial equation

Let N be an integer. Let a, b, A_1,...,A_N be constant real numbers. Let g(n) be a real function of integer variable n.

g(n) satisfies the recurrence equation:

(n + 1)(n + b)g(n+1) = (n + a)g(n) a)*g(n) + sum(i=1 to N)(A_iN)(A_i * g(n-i))

with g(n)=0 for n<0 . g(0) is obtained through boundary conditions, so it can be considered a given constant.

I need to know the general functional form of the term g(n), as a function of the given constants of the problem: a,b,N,A_1,...,A_N and g(0).

Could you help me? I could Could I programm in SAGE the code to provide the searched general term g(n)?