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+ | ====== LiouvillianSolution procedure ====== | ||

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+ | The procedure finds the Liouvillian solution of the given linear (q-)recurrence with the rational function coefficients using the algorithm by Hendriks & Singer. | ||

+ | The Liouvilian solution is a generalization of the (q-)hypergeometric solution. Let **H** is the set of all (q-)hypergeometric sequences and **L** is the smallest subring of the ring **S** of all sequences which contains **H | ||

+ | ** and is closed under (q-)shifts, summation and interlacing. The elements of **L** are called Liouvillian sequences and a recurrence has a Liouvillian solution if it has a nonzero solution in **L**. | ||

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+ | {{:liouvilliansolution.mm|LiouvillianSolution.mm}}- the Maple code of the procedure (implemented by D.E.Khmelnov and A.A.Ryabenko). | ||

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+ | {{:liouvilliansolution.mw|LiouvillianSolution.mw}} - the Maple session file help page and examples of using the procedure. | ||

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+ | {{:liouvilliansolution.pdf|LiouvillianSolution.pdf}} - PDF version of the Maple session file help page and examples of using the procedure. | ||

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