Singular values and fixed points of family of generating function of Bernoullis numbers


Authors

Mohammad Sajid - College of Engineering, Qassim University, Buraidah, Al-Qassim, Saudi Arabia.


Abstract

Singular values and fixed points of one parameter family of generating function of Bernoulli's numbers, \(g_\lambda(z) = \lambda\frac{z}{e^z-1} , \lambda\in \mathbb{R}-\{0\}\), are investigated. It is shown that the function \(g_\lambda(z)\) has infinitely many singular values and its critical values lie outside the open disk centered at origin and having radius \(\lambda\). Further, the real fixed points of \(g_\lambda(z)\) and their nature are determined. The results found are compared with the functions \(\lambda\tan z, E_\lambda(z) = \lambda \frac{e^z-1}{z}\) and\( f_\lambda(z) = \lambda \frac{z}{z+4}e^z\) for \(\lambda > 0\).


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ISRP Style

Mohammad Sajid, Singular values and fixed points of family of generating function of Bernoullis numbers, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 1, 17--22

AMA Style

Sajid Mohammad, Singular values and fixed points of family of generating function of Bernoullis numbers. J. Nonlinear Sci. Appl. (2015); 8(1):17--22

Chicago/Turabian Style

Sajid, Mohammad. "Singular values and fixed points of family of generating function of Bernoullis numbers." Journal of Nonlinear Sciences and Applications, 8, no. 1 (2015): 17--22


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