On the higher derivatives of the inverse tangent function | Zendy

Mohamed Amine Boutiche | Zendy; Mourad Rahmani | Zendy

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On the higher derivatives of the inverse tangent function

Author(s) -

Mohamed Amine Boutiche,

Mourad Rahmani

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1712-40

Subject(s) - inverse trigonometric functions , mathematics , fibonacci number , chebyshev polynomials , inverse , tangent , order (exchange) , fibonacci polynomials , inverse function , pure mathematics , function (biology) , recurrence relation , classical orthogonal polynomials , mathematical analysis , orthogonal polynomials , combinatorics , geometry , finance , evolutionary biology , economics , biology

In this paper, we find explicit formulas for higher order derivatives of the inverse tangent function. More precisely, we study polynomials which are induced from the higher-order derivatives of arctan(x). Successively, we give generating functions, recurrence relations and some particular properties for these polynomials. Connections to Chebyshev, Fibonacci, Lucas and Matching polynomials are established.

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