Abstract

In this article, two new subclasses of the bi-univalent function class σ related with Legendre polynomials are presented. Additionally, the first two Taylor–Maclaurin coefficients a2 and a3 for the functions belonging to these new subclasses are estimated.

Highlights

  • In 1782, Adrien-Marie Legendre discovered Legendre polynomials, which have numerous physical applications

  • Let A be the class of analytic functions in the open unit disc U = {z ∈ C : |z| < 1} with the following Taylor–Maclaurin series expansion

  • Lewin [5] is the first author who introduced the class of analytic bi-univalent functions and estimated the second coefficient | a2 |

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Summary

Introduction

In 1782, Adrien-Marie Legendre discovered Legendre polynomials, which have numerous physical applications. The Legendre polynomials Pn ( x ) are generated by the following function A general case of the Legendre polynomials and their applications can be found in [1,2]. Let A be the class of analytic functions in the open unit disc U = {z ∈ C : |z| < 1} with the following Taylor–Maclaurin series expansion

Results
Conclusion

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