Abstract
New sequences of orthogonal polynomials with respect to the weight functions \(e^{-x} \rho _\nu (x),\ e^{- 1/x} x^{-1} \rho _{\nu } (x), \rho _{\nu }(x)= 2 x^{\nu /2} K_\nu (2\sqrt{x}),\ x >0, \nu \in {\mathbb {R}}\), where \(K_\nu (z)\) is the modified Bessel function, are investigated. The recurrence relations, explicit representations, generating functions and Rodrigues-type formulae are obtained.
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Communicated by Dan Volok.
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The work was partially supported by CMUP [UID/MAT/00144/2019], which is funded by FCT(Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020, and Project STRIDE - NORTE-01-0145-FEDER- 000033, funded by ERDF - NORTE 2020. The author thanks Marco Martins Afonso for necessary numerical calculations and verifications of some formulas. Also sincere thanks to an anonymous referee for useful comments and suggestions which improved the presentation of the paper.
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Yakubovich, S. Orthogonal Polynomials with the Prudnikov-Type Weights. Complex Anal. Oper. Theory 14, 26 (2020). https://doi.org/10.1007/s11785-019-00973-4
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DOI: https://doi.org/10.1007/s11785-019-00973-4