Harmonic divisors and rationality of zeros of Jacobi polynomials
Files in This Item:
|Revised2RamanujanRender.pdf||179.3 kB||Adobe PDF||Download|
|Title:||Harmonic divisors and rationality of zeros of Jacobi polynomials||Authors:||Render, Hermann||Permanent link:||http://hdl.handle.net/10197/5488||Date:||Aug-2013||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||Copyright (published version):||2013 Springer||Keywords:||Jacobi polynomial;Dirichlet problem;Irreducible polynomial||DOI:||10.1007/s11139-013-9475-1||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
Show full item record
Page view(s) 5041
This item is available under the Attribution-NonCommercial-NoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. For other possible restrictions on use please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.