On the Macdonald-type function and its relation with index transforms and orthogonal polynomials
Year: 2026
Type: preprint
Abstract: We continue to investigate properties of the function $M_ν(z)$ which is associated with the Macdonald function $K_ν(z)$ in terms of the corresponding Fourier integral. In particular, recurrence relations for this function and its derivatives are obtained, involving properties of the associated Laguerre polynomials. Multiple orthogonal polynomials related to the scaled Macdonald-type weights $ \hatρ_ν(x)= 2 x^{ν/2} M_ν\left(2\sqrt x\right), x >0$ are investigated.
Source: arXiv (Cornell University)
Author: Yakubovich, Semyon
Institution: Universidade do Porto
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163664264
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