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CONCLUSIONS AND UNSOLVED PROBLEMS
analogue analytic function Bateman Bessel function boundary condition Bruwier Charlier polynomials complex variable Consider the solution continuous function contour integrals convergent Copson Corollary 16.2 deduce defined definition derivation difference equation differential equation discover Doetsch equa equal to zero equation 3.1 equation of type essay Euler transformation evaluate existence and uniqueness existence theorem expansion expl F(zQ familiar functions familiar special functions fixed value following theorem formal formula 1.1 formula 38 func function F(z functional equation given Hankel Hermite function Hypergeometric function Laguerre functions Laguerre polynomials Laplace transform linear Math Newton series obtain polynomials positive integer power series proved Q.E.D. Example reducible relation Rummer's first transformation satisfies the F-equation series solution solu Sonine Sonine's substitute solution substitute the solution Suppose F(z Taylor's theorem Theorem 9.1 theory tion transformation 1.17 uniqueness theorem valid Whittaker and Watson