On the interlacing of zeros of linear combinations of Jacobi polynomials from different sequences
نویسندگان
چکیده
We investigate the interlacing of the zeros of linear combinations pn+ aqm with the zeros of the components pn and qm, where {pn} ∞ n=0 and {qm} ∞ m=0 are different sequences of Jacobi polynomials. The results we prove hold when pn and qm are Jacobi polynomials P (α,β) n (x) and P (α,β) m (x) for certain values of α and β with m = n or m = n−1. Numerical counterexamples are given in situations where interlacing fails to occur. We also show that the zeros of the linear combination pn + aqm interlace with the zeros of some Jacobi polynomials besides the components of the linear combination. AMS MOS Classification: 33C45, 42C05.
منابع مشابه
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