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In this paper, we explore the asymptotic distribution of the zeros of the partial sums of the family of entire functions of order 1 and type 1, defined by G(μ,α,βz)=∫0 1μ(t)t α−1× (1−t)β−1e zt dt, where Re α,Re β>0, μ is Riemann-integrable on [0,1], continuous at t=0, 1 and satisfies μ(0)μ(1)≠0.
For those unfamiliar with it, the sci.math newsgroup hierarchy is a collection of thread-based bulletin boards dealing with all aspects of mathematics. Of that hierarchy, the group sci.math is devoted to the discipline in general. On any given day, topics posted there might be by high school or college students looking for help with homework, people… (More)
We examine the asymptotic behaviour of the zeros of sections of the binomial expansion. That is, we consider the distribution of zeros of B r,n (z) = r k=0 n k z k , where 1 ≤ r < n. A problem of great interest in the classical Complex Function Theory is the following: Given a function f (z) = ∞ k=0 a k z k , analytic at z = 0, determine the asymptotic… (More)
Although most books on the theory of complex variables include a classification of the types of isolated singularities, and the applications of residue theory, very few concern themselves with methods of computing residues. In this paper we derive some results on the calculation of residues at poles, and some special classes of essential singularities, with… (More)