On the Macdonald-type function and its relation with index transforms and orthogonal polynomials
Abstract
We continue to investigate properties of the function Mν(z) which is associated with the Macdonald function Kν(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 ρν(x)= 2 xν/2 Mν(2 x), x >0 are investigated.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.