return solution with a directly substituted hypergeometric term instead of a name representing it in the solution
SubstituteTerm(sol, term, n)
rational function in n and a name representing a hypergeometric term
The SubstituteTerm(sol, term, n) returns the solution with a directly substituted hypergeometric term instead of a name representing it in the solution.
The hypergeometric term in the linear difference equation is specified by a name, for example, t. The meaning of the term is defined by the parameter term. The term is specified as a list consisting of the name of the term variable and the consecutive term ratio, for example, t,n+1.
The solution is the function, corresponding to n. The solution involves arbitrary constants of the form, for example, _c1 and _c2.
eq ≔ y⁡n+2−n!+n⁢y⁡n+1+n⁢n!−1⁢y⁡n
sol,r ≔ PolynomialSolution⁡eq,y⁡n
sol,r ≔ t⁢_C1n,t,n+1
eq ≔ t+n2⁢z⁡n+1−2⁢n⁢t+2⁢t+n2+2⁢n+1⁢z⁡n
eq ≔ n2+t⁢z⁡n+1−n2+2⁢n⁢t+2⁢n+2⁢t+1⁢z⁡n
sol,r ≔ PolynomialSolution⁡eq,z⁡n,t=2n⁢n!
sol,r ≔ n2⁢_C1+t⁢_C1,t,2⁢n+2
Bronstein, M. "On solutions of Linear Ordinary Difference Equations in their Coefficients Field." INRIA Research Report. No. 3797. November 1999.
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