Journal•ISSN: 1617-9447
Computational Methods and Function Theory
Springer Science+Business Media
About: Computational Methods and Function Theory is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Meromorphic function & Bounded function. It has an ISSN identifier of 1617-9447. Over the lifetime, 922 publications have been published receiving 7289 citations. The journal is also known as: CMFT (Heidelberg. Internet) & Computational methods and function theory (Print).
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TL;DR: In this article, the best possible bounds for the weighted Holder mean of the generalized complete elliptic integrals of the first and second kinds are presented, which are generalizations of previous results for complete p-elliptic integral integrals.
Abstract: In the article, we present the best possible bounds for the weighted Holder mean of the zero-balanced generalized complete elliptic integrals of the first and second kinds, which are the generalizations of previous results for complete p-elliptic integrals.
162 citations
TL;DR: In this article, it was shown that Borel exceptional zeros and poles seem to appear in special situations only in the case of complex difference equations with rational rational rational solutions of finite order.
Abstract: In a recent paper [1], Ablowitz, Halburd and Herbst applied Nevanlinna theory to prove some results on complex difference equations reminiscent of the classical Malmquist theorem in complex differential equations. A typical example of their results tells us that if a complex difference equation y(z + 1) + y(z − 1) = R(z, y) with R(z, y) rational in both arguments admits a transcendental meromorphic solution of finite order, then degy R(z, y) ≤ 2. Improvements and extensions of such results are presented in this paper. In addition to order considerations, a result (see Theorem 13) is proved to indicate that solutions having Borel exceptional zeros and poles seem to appear in special situations only.
125 citations
TL;DR: In this paper, the authors consider Hardy space functions that vanish at the origin and obtain an exact positive Bohr radius, and show how renorming a space affects the Bohrradius.
Abstract: Bohr’s Theorem [10] states that analytic functions bounded by 1 in the unit disk have power series \(\sum a_n z^n\) such that \(\sum |a_n||z|^n<1\) in the disk of radius 1/3 (the so-called Bohr radius). On the other hand, it is known that there is no such Bohr phenomenon in Hardy spaces with the usual norm, although it is possible to build equivalent norms for which a Bohr phenomenon does occur. In this paper, we consider Hardy space functions that vanish at the origin and obtain an exact positive Bohr radius. Also, following [4, 11], we discuss the growth and Bohr phenomena for series of the type \(\sum |a_n|^p r^n\), \(0
118 citations
TL;DR: In this article, explicit analytical formulae for the conformal mappings from the canonical class of multiply connected circular domains to canonical classes of multiply-connected slit domains are constructed, which can be expressed in terms of the Schottky-Klein prime function associated with the multiplyconnected circular domains.
Abstract: Explicit analytical formulae for the conformal mappings from the canonical class of multiply connected circular domains to canonical classes of multiply connected slit domains are constructed. All the formulae can be expressed in terms of the Schottky-Klein prime function associated with the multiply connected circular domains.
113 citations
TL;DR: In this article, an introduction to basic parts of Clifford analysis including some historical remarks is given, along with an overview of the main parts of the Clifford analysis and some historical information.
Abstract: An introduction is given to basic parts of Clifford analysis including some historical remarks.
104 citations