return the universal denominator of the rational solutions for a difference equation depending on a hypergeometric term

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LREtools[HypergeometricTerm][UniversalDenominator] - return the universal denominator of the rational solutions for a difference equation depending on a hypergeometric term

	Calling Sequence
	UniversalDenominator(eq, var, term)

Parameters

eq	-	linear difference equation depending on a hypergeometric term
var	-	function variable for which to solve, for example, z(n)
term	-	hypergeometric term

Description

•	The PolynomialSolution(eq, var, term) command returns the universal denominator of the rational solution of the linear difference equation eq.

•

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. It can be specified directly in the form of an equation, for example, , or specified as a list consisting of the name of the term variable and the consecutive term ratio, for example, .

•	The term "rational solution" means a solution in . (See PolynomialSolution for the meaning of "polynomial solution".) Here we use the term "denominator" which is q in to mean that is in .

•	The search for a rational solution is based on finding a universal denominator which is u in such that is in for any rational solution y. By replacing y with in the given equation, we reduce the problem to searching for a polynomial solution.

Examples

(1)

(2)

eq := y(n+2)*n+4*y(n+2)*n*t+2*y(n+2)+4*y(n+2)*t+y(n+2)*t*n^2+y(n+2)*t^2*n^2+3*y(n+2)*n*t^2+2*y(n+2)*t^2-y(n)*n-y(n)*t*n^3-3*y(n)*t*n^2-2*y(n)*n*t-y(n)*t-y(n)*t^2*n^2-3*y(n)*n*t^2-2*y(n)*t^2

(3)

(4)

(5)

(6)

	See Also
	LREtools[HypergeometricTerm], LREtools[HypergeometricTerm][HGDispersion], LREtools[HypergeometricTerm][PolynomialSolution], LREtools[HypergeometricTerm][RationalSolution]