LREtools
AnalyticityConditions
analyticity conditions for the solution of linear difference equation.
Calling Sequence
Parameters
Description
Examples
References
AnalyticityConditions(L, E, fun, HalfInt_opt, Direction_opt)
L
-
linear difference operator in E with coefficients which are polynomials in x
E
name of the shift operator acting on x
fun
function f(x) that is a solution of
HalfInt_opt
(optional) 'HalfInterval'= A, A is a rational number, 0 by default
Direction_opt
(optional) 'direction'='left' -- the procedure returns the conditions for analyticity of f(x) on or 'direction'='right', the conditions on .
The AnalyticityConditions command returns the set of conditions for the analyticity of f(x).
The input includes a difference operator
L := sum(a[i](x)* E^i,i=1..d);
and a point A. The solution f(x) is analytic on some open set which contains a set . The procedure returns the set of conditions for the analyticity of f(x) on or if the option Direction_Opt is given or on the whole C otherwise. The conditions are linear relations of f(x) and, perhaps, several derivatives of f(x) at the points into .
solution f(x) = x is analytic everywhere on C:
solution f(x) = x->1/x^2 is not analytic anywhere on C:
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.
See Also
LREtools[IsDesingularizable]
LREtools[ValuesAtPoint]
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