Transactions of the American Mathematical Society · 1951 · 35 citations · 6 references
Bessel FunctionsAlgebraic PropertiesReal Algebraic GeometryOrthogonal PolynomialAnalytic Number TheorySymbolic Method (Combinatorics)Algebraic AnalysisAnalytic CombinatoricsBessel PolynomialsApproximation TheoryGeneralized BpAsymptotic Formula
which reduces to the first, for a = b = 2. H. L. Krall and 0. Frink called them polynomials(3) on account of their connection with the Bessel functions. They studied in detail properties of the BP and the generalized BP, such as recurrence relations, orthogonality, equivalent of Rodrigues' formula, generating function, and so on. In the present paper, we intend to establish some asymptotic formulas and to study algebraic properties of the BP. The main results are: (1) Let Yn(x) = (2n) !xnelIx/n!2n, Un(x) =exp (n2x/2). Then, for fixed x
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