Abstract:An entire function ƒ(z) is said to be of exponential type at most T iffor some z (and hence for every z, uniformly for z in any bounded set).An equivalent condition 2 is that for each positive € |/(2)...An entire function ƒ(z) is said to be of exponential type at most T iffor some z (and hence for every z, uniformly for z in any bounded set).An equivalent condition 2 is that for each positive € |/(2)| < e<r+ow for all sufficiently large \z\.The following three theorems were proved respectively by D. V. Widder [4], I. J. Schoenberg [2], and H. Poritsky [l] and J. M. Whittaker [3].Read More