On Classical Multiplier Sequences
We provide the detailed proofs of two recent claims of Csordas and Forgács asserting that two particular Bessel-type functions generate classical multiplier sequences whose generic terms are Cauchy-products of Laguerre polynomials and hypergeometric functions, respectively. The way these sequences are generated involves functions from the Laguerre-Pólya class. We address the question whether these functions are unique in any way as generators of a given classical multiplier sequence.
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