In this paper, we consider a random entire function f(s, ω) defined by a random Dirichlet series ∑∞ n=1Xn(ω)e −λns whereXn are independent and complex valued variables, 0 6 λn ր +∞. We prove that under natural conditions, for some random entire functions of order (R) zero f(s, ω) almost surely every horizontal line is a Julia line without an exceptional value. The result improve a theorem of J....

in this paper, we introduce the idea of relative order and type of entire functions represented by banach valued dirichlet series of two complex variables to generalize some earlier results.proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by dirichlet series is the same as that of it...

A general initial-boundary value problem of one-dimensional transient wave propagation in a multi-layered elastic medium due to arbitrary boundary or interface excitations (either prescribed tractions or displacements) is considered. Laplace transformation technique is utilised and the Laplace transform inversion is facilitated via an unconventional method, where the expansion of complex-valued...

Abstract Comparing phase plots of truncated series solutions Kepler’s equation by Lagrange’s power with those Bessel’s Kapteyn strongly suggests that a Jentzsch-type theorem holds true not only for the former but also latter series: each point boundary domain convergence in complex plane is cluster zeros sections series. We prove this result studying properties growth function sequence entire f...