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Singular Values of One Parameter Family of Generalized Generating Function of Bernoulli’s Numbers |
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PP: 2921-2924 |
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Author(s) |
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Mohammad Sajid,
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Abstract |
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| 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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