Journal of Integer Sequences, Vol. 26 (2023), Article 23.1.3

Some New Identities for Arctangents and Chebyshev Polynomials

Jiejie Gao
School of Mathematics
Northwest University
Xi'an, Shaanxi


In this paper, we use some properties of Chebyshev polynomials and trigonometric functions to study four classes of sums of products of two arctangents involving these polynomials. We also give some infinite series identities concerning Fibonacci and Lucas numbers.

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(Concerned with sequences A000032 A000045.)

Received August 31 2022; revised versions received September 16 2022; December 20 2022. Published in Journal of Integer Sequences, January 1 2023.

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