Abstract
Singular values and fixed points of one parameter family of generating function of Bernoulli's numbers, g(lambda)(z) = lambda z/e(z-)1, lambda is an element of 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 A. 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 e(z)-1/z and f(lambda)(z) = lambda z/z+4 e(z) for lambda > 0. (C) 2015 All rights reserved.