Some Identities Involving the Reciprocal Sums of One‐Kind Chebyshev Polynomials

Abstract

We use the elementary and analytic methods and the properties of Chebyshev polynomials to study the computational problem of the reciprocal sums of one-kind Chebyshev polynomials and give several interesting identities for them. At the same time, we also give a general computational method for this kind of reciprocal sums.

On the Sums of Powers of Chebyshev Polynomials and Their Divisible Properties

“…See [1][2][3][4][5][6][7][8][9][10][11]. For example, Li [1] proved some identities involving power sums of ( ) and ( ).…”

“…She obtained some divisibility properties involving Chebyshev polynomials as some applications of these results. Ma and Lv [2] studied the computational problem of the reciprocal sums of Chebyshev polynomials and obtained some identities. Some theoretical results related to Chebyshev polynomials can be found in Ma and Zhang [3], Cesarano [4], Lee and Wong [5], Bhrawy and others (see [6][7][8][9]), and Wang and Zhang [10].…”

The Power Sums Involving Fibonacci Polynomials and Their Applications

“…Since the Fibonacci numbers and Lucas numbers occupy significant positions in combinatorial mathematics and elementary number theory, they are thus studied by plenty of researchers, and have gained a large number of vital conclusions; some of them can be found in References [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For example, Yi Yuan and Zhang Wenpeng [1] studied the properties of the Fibonacci polynomials, and proved some interesting identities involving Fibonacci numbers and Lucas numbers.…”

Some Symmetric Identities Involving Fubini Polynomials and Euler Numbers

“…Therefore, several scholars have researched their various properties, and acquired a series of vital results. Some involved contents can be found in references [5,[7][8][9][10][11][12][13][14][15][16][17].…”