Interlacing of zeros of linear combinations of classical orthogonal polynomials from different sequences

Authors:
Kathy Driver;Kerstin Jordaan;Norbert Mbuyi
Affiliations:
Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X3, Rondebosch 7701, Cape Town, South Africa;Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa;Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

We prove that the zeros of polynomials of consecutive degree in the sequences {r"n}"n"="1^~ and {s"n}"n"="1^~ are interlacing for n@?N, n=1 wherer"n=p"n+a"nq"n,s"n=p"n+b"nq"n"-"1,a"n,b"n0,a"n,b"n@?R and {p"n}"n"="1^~ and {q"n}"n"="1^~ are different sequences of Laguerre (respectively Jacobi) polynomials.