LREtools[AnalyticityConditions] - analyticity conditions for the solution of linear difference equation.
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Calling Sequence
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AnalyticityConditions(L, E, fun, HalfInt_opt, Direction_opt)
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Parameters
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L
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linear difference operator in E with coefficients which are polynomials in x
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E
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name of the shift operator acting on x
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fun
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function f(x) that is a solution of
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HalfInt_opt
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(optional) 'HalfInterval'= A, A is a rational number, 0 by default
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Direction_opt
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(optional) 'direction'='left' -- the procedure returns the conditions for analyticity of f(x) on or 'direction'='right', the conditions on .
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Description
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The AnalyticityConditions command returns the set of conditions for the analyticity of f(x).
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The input includes a difference operator
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L := sum(a[i](x)* E^i,i=1..d);
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Examples
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solution f(x) = x is analytic everywhere on C:
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solution f(x) = x->1/x^2 is not analytic anywhere on C:
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References
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Abramov, S.A., and van Hoeij, M. "Set of Poles of Solutions of Linear Difference Equations with Polynomial Coefficients." Computation Mathematics and Mathematical Physics. Vol. 43 No. 1. (2003): 57-62.
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