A NEW EXPLICIT BOUND IN LANDAU THEOREM

Let f(z) = a0 + a1z + ... be holomorphic in the unit disk {z: Absolute value of z <1} and omit the values 0 and 1. It is proved in this paper that \a1\less-than-or-equal-to 2\a0\{log\a0\\ + GAMMA4(1/4)/4pi2 - mRe(a0epsilon + 1)} where m>0.04 is a constant, epsilon=1 as \a0\less-than-or-equal-to 1 and epsilon = -1 as \a0\>1. This result is a precise version of the well-known theorem of Landau and an improvement of the results of W. Lai[1], J. A. Hempel[2] and J. A. Jenkins[3].Mathematics, AppliedMathematicsSCI(E)1ARTICLE8897-9063