Abstract
Delsarte’s approach to generalized translation operators via the solution of an associated Cauchy problem is used to derive the product formulas for the Bessel, Whittaker, and Jacobi functions in kernel form. As essential prerequisites, explicit representations of the corresponding Riemann functions are given for three cases. The main part of the paper deals with the Jacobi case, for which the derivation of the translation kernel is carried out explicitly. In the Bessel case, the results of Delsarte are covered, and in the Whittaker case, a generalization of previous results of the author on the Laguerre polynomial product formula is obtained.
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Supported by the Deutsche Forschungsgemeinschaft under grant No. Go 261/5–2.
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Markett, C. (1984). Product Formulas for Bessel, Whittaker, and Jacobi Functions via the Solution of an Associated Cauchy Problem. In: Butzer, P.L., Stens, R.L., Sz.-Nagy, B. (eds) Anniversary Volume on Approximation Theory and Functional Analysis. ISNM 65: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 65. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5432-0_39
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DOI: https://doi.org/10.1007/978-3-0348-5432-0_39
Publisher Name: Birkhäuser, Basel
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