Matrix transformation of univalent power series

Univalent functions of fast growth with gap power series

We construct univalent functions in the unit disc, whose coefficient sequences (an) have arbitrarily long intervals of zeros, and at the same time arbitrarily long intervals where |an| > n n holds, ( n) being an an arbitrary prescribed sequence of positive numbers tending to zero. Furthermore we show that the initial interval of coefficients of such a function can be prescribed to be any interi...

Variance Stabilizing Power Transformation for Time Series

Hankel matrix transformation of the Walsh-Fourier series

The Hankel matrix has various applications. In this paper we prove that Hankel matrix is strongly regular and apply to obtain the necessary and sufficient conditions to sum the Walsh–Fourier series of a function of bounded variation. 2013 Elsevier Inc. All rights reserved.

Analysis of Convergence of the T-Transformation for Power Series

Recently the present author has given some convergence theorems of general nature for Levin's nonlinear sequence transformations. In this work these theorems are extended and sharpened to cover the case of power series, both inside and on their circle of convergence. It is shown that one of the two limiting processes considered in the previous work can be used for analytic continuation and a re...

A Symbolic Operator Approach to Power Series Transformation-Expansion Formulas

Here expounded is a kind of symbolic operator method by making use of the defined Sheffer-type polynomial sequences and their generalization, which can be used to construct many power series transformation and expansion formulas. The convergence of the expansions are also discussed. AMS Subject Classification: 41A58, 41A80, 65B10, 05A15, 33C45, 39A70.