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- W2022334967 abstract "Consider the inner product[email protected](@[email protected]+2)2^@a^+^@b^+^[email protected](@a+1)@C(@b+1)@!-11p(x)q(x)(1-x)^@a(1+x)^@bdx+Mp(1)q(1)+Np^'(1)q^'(1)[email protected]?p(-1)q(-1)[email protected]?p^'(-1)q^'(-1) where @a,@b>-1 and M,N,[email protected]?,[email protected]?>=0. If @m=(M,N,[email protected]?,[email protected]?), we denote by xn,k^@m(@a,@b), k=1,...,n, the zeros of the n-th polynomial Pn^(^@a^,^@b^,^@m^)(x), orthogonal with respect to the above inner product. We investigate the location, interlacing properties, asymptotics and monotonicity of xn,k^@m(@a,@b) with respect to the parameters M,N,[email protected]?,[email protected]? in two important cases, when either [email protected][email protected]?=0 or [email protected]?=0. The results are obtained through careful analysis of the behavior and the asymptotics of the zeros of polynomials of the form pn(x)=hn(x)+cgn(x) as functions of c." @default.
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- W2022334967 date "2010-03-01" @default.
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- W2022334967 title "Monotonicity of zeros of Jacobi–Sobolev type orthogonal polynomials" @default.
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- W2022334967 doi "https://doi.org/10.1016/j.apnum.2009.12.004" @default.
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