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The Ratio Monotonicity of the q-Derangement Numbers
q-derangement number spiral property log-concavity ratio monotone property
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2014/6/3
We introduce the notion of ratio monotonicity for polynomials with nonnegative coefficients, and we show that for n ≥ 6, the q-derangement numbers Dn(q) are strictly ratio monotone, except for the las...
Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences
log-concavity ratio monotonicity Boros-Moll polynomials
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2014/6/3
The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P(x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P(x ...
The Ratio Monotonicity of the Boros-Moll Polynomials
ratio monotone property spiral property unimodality log-concavity Jacobi polynomials Boros-Moll polynomials
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2014/6/3
In their study of a quartic integral, Boros and Moll discovered a special class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers and Paule proved the conjecture of Moll that the...