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Applied Mathematics & Information Sciences

Author Country (or Countries)

Saudi Arabia

Abstract

The goal of this paper is to describe the singular values of one parameter family of generalized generating function of Bernoulli’s numbers, fl (z) =l z bz−1 , fl (0) = l lnb for l ∈ R\{0}, z ∈ C and b > 0 except b = 1. It is found that the function fl (z) has an infinite number of singular values for all b > 0 except b = 1. Further, it is shown that all the critical values of fl (z) belongs to the exterior of the disk centered at origin and having radius | l lnb | in the right half plane for 0 < b < 1 and in the left half plane for b > 1 respectively.

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