Improved Bounds for Taylor Coefficients of Analytic Functions

Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions

In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].

On the Taylor Coefficients of Rational Functions

Two-point Taylor Expansions of Analytic Functions

In deriving uniform asymptotic expansions of a certain class of integrals one encounters the problem of expanding a function, that is analytic in some domain Ω of the complex plane, in two points. The first mention of the use of such expansions in asymptotics is given in [1], where Airy-type expansions are derived for integrals having two nearby (or coalescing) saddle points. This reference doe...

On the Taylor Coefficients of the Composition of Two Analytic Functions

We give an asymptotic formula for the Taylor coeecients f n of f(z) = l(h(z)) where l(z) is analytic in the unit disc whose Taylor coeecients l n vary`smoothly' and h(z) is analytic in a larger disc. We show that under mild conditions on h(z) , f n l n] as n ! 1 where = 1=h 0 (1). Applications to renewal theory are also discussed.

Multi-point Taylor Expansions of Analytic Functions

Abstract. Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obt...