Interlacing of zeros of Laguerre polynomials of equal and consecutive degree
نویسندگان
چکیده
We investigate interlacing properties of zeros Laguerre polynomials Ln(α)(x) and Ln+1(α+k)(x), α>−1, where n∈N k∈{1,2}. prove that, in general, the these interlace partially not fully. The sharp t-interval within which two equal degree Ln(α+t)(x) are for every each α>−1 is 0−1. Numerical illustrations its breakdown provided.
منابع مشابه
Stieltjes interlacing of zeros of Laguerre polynomials from different sequences
Stieltjes’ Theorem (cf. [11]) proves that if {pn}n=0 is an orthogonal sequence, then between any two consecutive zeros of pk there is at least one zero of pn for all positive integers k, k < n; a property called Stieltjes interlacing. We prove that Stieltjes interlacing extends across different sequences of Laguerre polynomials Ln, α > −1. In particular, we show that Stieltjes interlacing holds...
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ژورنال
عنوان ژورنال: Integral Transforms and Special Functions
سال: 2021
ISSN: ['1476-8291', '1065-2469']
DOI: https://doi.org/10.1080/10652469.2020.1804901