Singular Values of One Parameter Family lambda b(z-1)/z

The singular values of one parameter family of entire functions f(lambda)(z) = lambda b(z) -1/z and f(lambda) (0) = lambda lnb, lambda is an element of R\ {0}, z is an element of C, b > 0, b not equal 1 are investigated. It is shown that all the critical values of f(lambda)(z) belong to the right half plane for 0<b<1 and the left half plane for b > 1. It is described that the function f(lambda)(z) has infinitely many singular values. It is also found that all these singular values are bounded and lie inside the open disk centered at origin and having radius vertical bar lambda lnb vertical bar.