Proceedings of the American Mathematical Society · 1953 · 14 citations · 0 references
Natural SciencesMathematicsCombinatoricsDifferential EquationsPattern FormationGenerating FunctionsSpecial FunctionsBessel FunctionsOrthogonal ExpansionsOrthogonal Polynomial ExpansionsOrthogonal PolynomialsRational Generating Functions
Received by the editors June 23, 1952. 1 H. L. Krall and Orrin Frink, A new class of orthogonal polynomials; the Bessel polynomials, Trans. Amer. Math. Soc. vol. 65 (1949) pp. 100-115. 2 See J. L. Burchnall, The Bessel polynomials, Canadian Journal of Mathematics vol. 3 (1951) pp. 62-68, and E. D. Rainville, Generating functions for Bessel and related polynomials, Canadian Journal of Mathematics vol. 5 (1953) pp. 104-106. 3 Each 2Fo in (3) diverges except for nonpositive integer parameters or for zero argument. Equation (3) means that the coefficient of each power of t on the left equals the coefficient of the corresponding power on the right. Fortunately convergence is not in general necessary in using generating functions.