Applications of Beta Negative Binomial Distribution and Laguerre Polynomials on Ozaki Bi-Close-to-Convex Functions

Abstract

In the present paper, due to beta negative binomial distribution series and Laguerre polynomials, we investigate a new family FΣ(δ,η,λ,θ;h) of normalized holomorphic and bi-univalent functions associated with Ozaki close-to-convex functions. We provide estimates on the initial Taylor–Maclaurin coefficients and discuss Fekete–Szegő type inequality for functions in this family.

Keywords

• bi-univalent function
• Laguerre polynomial
• coefficient bound
• Fekete–Szegő problem
• beta negative binomial distribution
• subordination