In this present investigation, we consider the subclass of analytic and bi-univalent functions associated with salagean operator consisting of the function class Σ in the unit open disk, which satisfies the qusi-subordination conditions. Also we obtain the first two Taylor-Maclaurin coefficients for functions in this new subclass. Mathematics Subject Classification: 30C45, 30C50

in this paper, we will compare a homotopy perturbation algorithm and taylor series expansin method for a system of second kind fredholm integral equations. an application of he’s homotopy perturbation method is applied to solve the system of fredholm integral equations. taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

In this paper, we have introduced and investigated two new subclasses of the function class Δ of bi-univalent functions defined in the open unit disk, which are associated with the generalized Hypergeometric function. Furthermore, we find estimates on the Taylor-Maclaurin coefficient | a2 | and | a3 | for the functions belonging to these new classes.

In this paper, we introduce and investigate a new subclass of biunivalent functions ∑ of complex order defined in the open unit disk, which are associated with hypergeometric functions and satisfy subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients 2 | | a and 3 | | a for functions in the new subclass. Several (known or new) consequences of the results ar...

We introduce and investigate an interesting subclass NP(λ,δ)(Σ) (n, β; h) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class NP(λ,δ)(Σ) (n, β; h), we obtain estimates on the first two Taylor-Maclaurin coefficients |a₂| and |a₃|.

We study a connection between Euler-MacLaurin Summation and Boole Summation suggested in an AMM note from 1960, which explains them as two cases in a general approach to approximation that also encompasses Taylor sums. Here we give additional details of the construction.

In this paper, we study the departure process of the GI/G/1 queue. We develop a simple recursive procedure to calculate the MacLaurin series of its moments and covariances with respect to a parameter in the service time. Based on this recursive procedure the explicit formulas of the coeÆcients of these MacLaurin series can be obtained in terms of derivatives of the probability density function ...

In this article, we establish the bounds for initial Taylor–Maclaurin coefficients |a2| and |a3| a new family G?(?,?,?;h) of holormorphic bi-univalent functions which involve prestarlike functions. Furthermore, investigate Fekete–Szegö type inequality, special cases consequences.

In the contemporary paper, we introduce new subclasses of analytic and bi-univalent functions involving integral operator based upon Lucas polynomial. Furthermore, find estimates on first two Taylor-Maclaurin coefficients a2 a3 for in these obtain Fekete-Szegö problem subclasses.