平衡多项式与第一类和第二类切比雪夫多项式的超几何联系

IF 0.5 Q3 MATHEMATICS Armenian Journal of Mathematics Pub Date : 2022-09-23 DOI:10.52737/18291163-2022.14.12-1-20

A. Behera, P. Ray

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引用次数: 0

摘要

在本研究中，我们发现了平衡多项式与第一类和第二类切比雪夫多项式之间的几个联系。第一类和第二类切比雪夫多项式表示为具有超几何系数的平衡多项式的两项之和。作为反演，平衡多项式也表示为具有超几何系数的第一类Chebyshev多项式和第二类Cheby雪v多项式的两项之和。

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Hypergeometric connections between balancing polynomials and Chebyshev polynomials of first and second kinds

In the present study, we find several connections between balancing polynomials and the Chebyshev polynomials of the first and second kinds. The Chebyshev polynomials of the first and second kinds are expressed as the sum of two terms of balancing polynomials with hypergeometric coefficients. As an inversion, the balancing polynomials are also expressed as the sum of two terms of the Chebyshev polynomials of the first kind and the Chebyshev polynomials of the second kind with hypergeometric coefficients.

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