Generalizing Certain Analytic Functions Correlative to the n-th Coefficient of Certain Class of Bi-Univalent Functions

In the present paper, the authors implement the two analytic functions with its positive real part in the open unit disk. New types of polynomials are introduced, and by using these polynomials with the Faber polynomial expansion, a formula is structured to solve certain coefficient problems. This formula is applied to a certain class of bi-univalent functions and solve the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>n</a:mi> </a:math> -th term of its coefficient problems. In the last section of the article, several well-known classes are also extended to its <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>n</c:mi> </c:math> -th term.