The first and second kind chebyshev coefficients of the moments for the general order derivative on an infinitely differentiable function

Fekete-Szegö inequality for analytic and bi-univalent functions subordinate to Chebyshev polynomials

“…These orthogonal polynomials, in a real variable t and a complex variable z, have played an important role in applied mathematics, numerical analysis and approximation theory. For this reason, Chebyshev polynomials have been studied extensively, see [8,10,16]. In the study of differential equations, the Chebyshev polynomials of the first and second kinds are the solution to the Chebyshev differential equations (1 − t 2 )y ′′ − ty ′ + n 2 y = 0 (1.1) and (1 − t 2 )y ′′ − 3ty ′ + n(n + 2)y = 0, (1.2) respectively.…”

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“…In Koegh and Merkes [10], solved the Fekete-Szegö problem for the classes of starlike and convex functions for some real  . The Fekete-Szegö problem has been investigated by many mathematicians for several subclasses of analytic functions [8,[11][12][13][14][15][16][17][18].…”

A comprehensive subclass of bi-univalent functions associated with Chebyshev polynomials of the second kind

“…They have abundant properties, which make them useful in many areas in applied mathematics, numerical analysis and approximation theory. There are four kinds of Chebyshev polynomials, see for details Doha [12] and Mason [20]. The Chebyshev polynomials of degree n of the second kind, which are denoted U n (t), are defined for t ∈ [−1, 1] by the following three-terms recurrence relation:…”