The hole probability for Gaussian entire functions

Probability Generating Functions for Sattolo’s Algorithm

In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the ...

The Degree of Convergence for Entire Functions

Consider a Doint set C in the complex plane whose complement K is connected and regular (i .e. K possesses a Green ' s function with pole at infini ty). Let denote the transfini te diameter of C . Recall that d m = l /U ' C®)! where <{>(z) irans >C onto tl ê exterior of the uni t circle. Equivalent ly , d^ = Lin | |T^(z) | Ij.] where | |g(z) | | c = max] <*(z) | ,zeC and T..(z) is t^e Tchebyche...

Products and Convolutions of Gaussian Probability Density Functions

Growth analysis of entire functions of two complex variables

In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

Prime Entire Functions

Factorizations of various functions are discussed. Complete factorizations of certain classes of functions are given. In particular it is shown that there exist primes of arbitrary growth.