Regular Analytic Transformations of R 2

P-symbols, Heun Identities, and 3 F 2 Identities

The usefulness of Riemann P-symbols in deriving identities involving the parametrized special function Hl is explored. Hl is the analytic local solution of the Heun equation, the canonical second-order differential equation on the Riemann sphere with four regular singular points. The identities discussed include ones coming from Möbius automorphisms and F-homotopies, and also quadratic and biqu...

Ellipses, near Ellipses, and Harmonic Möbius Transformations

It is shown that an analytic function taking circles to ellipses must be a Möbius transformation. It then follows that a harmonic mapping taking circles to ellipses is a harmonic Möbius transformation. Analytic Möbius transformations take circles to circles. This is their most basic, most celebrated geometric property. We add the adjective ‘analytic’ because in a previous paper [1] we introduce...

Some properties of extended multiplier transformations to the classes of meromorphic multivalent functions

 In this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{T}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. We use a strong convolution technique and derive inclusion results. A radius problem and some other interesting properties of these classes are discussed.

FACTOR TRANSFORMATIONS : ANALYTIC TRANSFORMATIONS From Exploratory Factor Analysis

Extrapolating Tree Transformations

We consider the framework of regular tree model checking where sets of configurations of a system are represented by regular tree languages and its dynamics is modeled by a term rewriting system (or a regular tree transducer). We focus on the computation of the reachability set R(L) where R is a regular tree transducer and L is a regular tree language. The construction of this set is not possib...