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Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

Luchko, Yury (2008)

Fractional Calculus and Applied Analysis

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15The paper deals with analysis of several techniques and methods for the numerical evaluation of the Wright function. Even if the focus is mainly on the real arguments’ values, the methods introduced here can be used in the complex plane, too. The approaches presented in the paper include integral representations of the Wright function, its asymptotic expansions and summation of series. Because the Wright function depends on two parameters ...

Almost Abelian regular dessins d'enfants

Ruben A. Hidalgo (2013)

Fundamenta Mathematicae

A regular dessin d'enfant, in this paper, will be a pair (S,β), where S is a closed Riemann surface and β: S → ℂ̂ is a regular branched cover whose branch values are contained in the set {∞,0,1}. Let Aut(S,β) be the group of automorphisms of (S,β), that is, the deck group of β. If Aut(S,β) is Abelian, then it is known that (S,β) can be defined over ℚ. We prove that, if A is an Abelian group and Aut(S,β) ≅ A ⋊ ℤ₂, then (S,β) is also definable over ℚ. Moreover, if A ≅ ℤₙ, then we provide explicitly...

Alternative Characterization of the Class k-UCV and Related Classes of Univalent Functions

Kanas, Stanislawa (1999)

Serdica Mathematical Journal

In this paper an alternative characterization of the class of functions called k -uniformly convex is found. Various relations concerning connections with other classes of univalent functions are given. Moreover a new class of univalent functions, analogous to the ’Mocanu class’ of functions, is introduced. Some results concerning this class are derived.

An algebraic addition-theorem for Weierstrass' elliptic function and nomograms

Akira Matsuda (1979)

Aplikace matematiky

A dual transformation is discussed, by which a concurrent chart represented by one equation is transformed into an alignment chart or into a tangential contact chart. Using this transformation an alignment chart where three scales coincide and a tangential contact chart consisting of a family of circles, which represent the relation u + v + w = 0 , are constructed. In this case, a form of the addition-theorem for Weierstrass’ function involving no derivative is used.

An analogue of Montel’s theorem for some classes of rational functions

R. K. Kovacheva, Julian Lawrynowicz (2002)

Czechoslovak Mathematical Journal

For sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of the best L p -approximation with an unbounded number of finite poles are considered.

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