Consider the function defined for $\alpha _{1},\ \alpha _{2} \in \mathbb{R}$ (α 1 2 +α 2 2 ≠ 0) and $\beta _{1},\beta _{2} \in \mathbb{C}$ by the series 

$$\displaystyle{ E_{\alpha _{1},\beta _{1};\alpha _{2},\beta _{2}}(z) \equiv \sum _{k=0}^{\infty } \frac{z^{k}} {\varGamma (\alpha _{1}k +\beta _{1})\varGamma (\alpha _{2}k +\beta _{2})}\ \ (z \in \mathbb{C}). }$$

(6.1.1)

Such a function with positive α 1 > 0, α 2 > 0 and real $\beta _{1},\beta _{2} \in \mathbb{R}$ was introduced by Dzherbashian [Dzh60].

Multi-index Mittag-Leffler Functions

We provide an overview of such properties of the Brownian motion on complete non-compact Riemannian manifolds as recurrence and non-explosion. It is shown that both properties have various analytic characterizations, in terms of the heat kernel, Green function, Liouville properties etc. On the other hand, we consider a number of geometric conditions such as the volume growth, isoperimetric inequalities, curvature bounds etc. which are related to recurrence and non-explosion.

/pdf/analytic-and-geometric-background-of-recurrence-and-non-52dn9fdnqn.pdf

Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds

On subharmonic functions and differential geometry in the large

http://misgam.sissa.it/papers/files/MIS0112.pdf

Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations

The theorem of Picard in its simplest form asserts that every nonconstant functionf (z), meromorphic in the plane, assumes there all complex values w with the possible exception of two. A value w which is not assumed by f(z) will be called a Picard value. The problem of our paper concerns the possible relationships between Picard values of f(z) and its derivatives. Let us first consider integral functions. Here the complete result is the following, due to Milloux [2], though special cases go back to Saxer [4].

Picard Values of Meromorphic Functions and their Derivatives

Eindeutige Analytische Funktionen

Le théorème de Picard-Borel et la théorie des fonctions méromorphes

/pdf/einige-eindeutigkeitssatze-in-der-theorie-der-meromorphen-41a3t7a1sz.pdf

Einige Eindeutigkeitssätze in der Theorie der Meromorphen Funktionen

/pdf/zur-theorie-der-meromorphen-funktionen-2bk5kyy6l4.pdf

Rolf Nevanlinna

Papers

Eindeutige Analytische Funktionen

Le théorème de Picard-Borel et la théorie des fonctions méromorphes

Einige Eindeutigkeitssätze in der Theorie der Meromorphen Funktionen

Zur Theorie der Meromorphen Funktionen

Über die Nullstellen der Riemannschen Zetafunktion