Harmonic divisors and rationality of zeros of Jacobi polynomials

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Title: Harmonic divisors and rationality of zeros of Jacobi polynomials
Authors: Render, Hermann
Permanent link: http://hdl.handle.net/10197/5488
Date: Aug-2013
Online since: 2014-03-27T15:47:30Z
Abstract: Let Pn (α,β ) ( x ) be the Jacobi polynomial of degree n with parameters αβ The main result of the paper states the following: If b≠ 1 ; 3 and c are non-zero rel- atively prime natural numbers then P ( k +( d 3) = 2 ;k +( d 3) = 2) n p b=c 6 ≠ 0 for all natural numbers d;n and k 2 N 0 : Moreover, under the above assumption, the polynomial Q ( x ) = b c x 2 1 + ::: + x 2 d 1 + b c 1 x 2 d is not a harmonic divisor, and the Dirichlet problem for the cone f Q ( x ) < 0 g has polynomial harmonic solutions for polynomial data functions.
Type of material: Journal Article
Publisher: Springer
Journal: Ramanujan Journal
Volume: 31
Issue: 3
Start page: 257
End page: 270
Copyright (published version): 2013 Springer
Keywords: Jacobi polynomialDirichlet problemIrreducible polynomial
DOI: 10.1007/s11139-013-9475-1
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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