## Linear Difference Equations and Their Analytic Solutions |

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a*xm absolute value different analytic function analytic in D2 analytic solutions analytic throughout D2 approaches infinity arbitrary periodic functions axis of reals bounding the increase characteristic equation circle CKRH closed region cofactor constant term contour integral converging series corresponding determined difference equation different from zero entire function evident existence theorem finite plane fn(x following inequalities formal solution functions of period fundamental system Hence identically zero increase or decrease inequalities 40 Inequalities bounding integrand IP(x line parallel London Mathematical Society method of successive normal form normal system P-region particular solution path of integration points congruent positive direction principal results properly chosen constant real axis region Dx set of points single-valued solution of 24 solutions 77 substitution successive approximation system of equations system of solutions term in 1/x throughout any closed throughout the finite tions transformation 83 uniformly convergent upper bound x approaches infinity Z)-region