Singular Values of One Parameter Family \(\lambda ((e^{z}-1)/z)^{m}\)

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    In the present paper, the singular values of one parameter family of entire functions \(f_{\lambda}(z)=\lambda\bigg(\dfrac{e^{z}-1}{z}\bigg)^{m}\) and \(f_{\lambda}(0)=\lambda\), \(m\in \mathbb{N}\backslash \{0\}\), \(\lambda\in \mathbb{R} \backslash \{0\}\), \(z \in \mathbb{C}\) is investigated. It is shown that all the critical values of \(f_{\lambda}(z)\) lie in the left half plane. It is also found that the function \(f_{\lambda}(z)\) has infinitely many bounded singular values and lie inside the open disk centered at origin and having radius \(|\lambda|\).

  • Keywords


    Critical values; Singular values

  • References


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Article ID: 4359
 
DOI: 10.14419/ijamr.v4i2.4359




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