Record number :
1529703
Title of article :
Convolutions and zeros of orthogonal polynomials
Author/Authors :
Area، نويسنده , , Ivلn and Dimitrov، نويسنده , , Dimitar K. and Godoy، نويسنده , , Eduardo، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2011
Pages :
11
From page :
868
To page :
878
Abstract :
In an attempt to answer a long standing open question of Al-Salam we generate various beautiful formulae for convolutions of orthogonal polynomials similar to U n ( x ) = ∑ k = 0 n P k ( x ) P n − k ( x ) , where U n ( x ) are the Chebyshev polynomials of the second kind and P k ( x ) are the Legendre polynomials. The results are derived both via the generating functions approach and a new convolution formulae for hypergeometric functions. We apply some addition formulae similar to the well-known expansion H n ( x + y ) = 2 − n / 2 ∑ k = 0 n ( n k ) H k ( 2 x ) H n − k ( 2 y ) for the Hermite polynomials, due to Appell and Kampé de Fériet, to obtain new interesting inequalities about the zeros of the corresponding orthogonal polynomials.
Keywords :
convolution , orthogonal polynomials , generating function , Zeros
Journal title :
Applied Numerical Mathematics
Serial Year :
2011
Link To Document :
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