On Hadamard's Factorization Theorem

In a paper published in 1927, Landau gave a new proof of Hadamard's theorem on the factorization of an integral function of finite order. His proof arose out of the study of the problem of factorization of (s-I)ζ(s), which had been for the first time solved by Hadamard and for which Ananda Rau gave an alternative proof by the use of Gauchy's theorem of residues. The object of this paper is to combine the methods of Landau and Ananda Rau to obtain another proof of Hadamard's general theorem of factorization.