Taylor coefficients of smooth functions

On the Taylor Coefficients of Rational 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].

Initial coefficients of starlike functions with real coefficients

The sharp bounds for the third and fourth coefficients of Ma-Minda starlike functions having fixed second coefficient are determined. These results are proved by using certain constraint coefficient problem for functions with positive real part whose coefficients are real and the first coefficient is kept fixed. Analogous results are obtained for a general class of close-to-convex functions

The decay of the Walsh coefficients of smooth functions

We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown. Mathematical Subject Classification (2000): P...

Automatic asymptotics for coefficients of smooth, bivariate rational functions

We consider a bivariate rational generating function F (x, y) = P (x, y) Q(x, y) = ∑ r,s≥0 arsx y under the assumption that the complex algebraic curve V on which Q vanishes is smooth. Formulae for the asymptotics of the coefficients {ars} are derived in [PW02]. These formulae are in terms of algebraic and topological invariants of V, but up to now these invariants could be computed only under ...