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polynomials that have golden ratio zeros
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نویسنده
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maier jack ,he tian-xiao ,vanness kurt
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منبع
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journal of advanced mathematical studies - 2014 - دوره : 7 - شماره : 1 - صفحه:151 -175
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چکیده
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When the golden ratio and its conjugate are zeros to a polynomial, two of the coefficients are functions of the fibonacci sequence in terms of the other coefficients, which characterize the polynomial completely. these functions are used to derive some fn, ln, and golden ratio identities. in many cases, this is generalized to the lucas sequences un and vn, with an associated quadratic root pair. horadam sequences are produced in the the series of linear and constant coefficients of the series of polynomials having ra and rb zeros when all of the other coefficients are equal.
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کلیدواژه
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fibonacci sequence ,lucas sequence ,horadam sequence ,golden ratio
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آدرس
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wesleyan university, department of mathematics, usa, wesleyan university, department of mathematics, usa
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پست الکترونیکی
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kvanness@iwu.edu
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Authors
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