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01-Applied Mathematics & Information Sciences
An International Journal
               
 
 
 
 
 
 
 
 
 
 
 

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Volumes > Volume 9 > No. 6

 
   

Singular Values of One Parameter Family of Generalized Generating Function of Bernoulliís Numbers

PP: 2921-2924
Author(s)
Mohammad Sajid,
Abstract
The goal of this paper is to describe the singular values of one parameter family of generalized generating function of Bernoulliís 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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