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is a Hurwitz polynomial(2). This method is extended in this paper to an algorithm for counting the number of zeros of P(z) with positive and negative real parts (?2). A different method for the determination of these numbers has been given by Frank [3] and Bilharz [1] in terms of determinants and another by Frank [3] in terms of continued fractions. In ?3, a method is given for the computation of the zeros of P(z) by an application of the algorithm of ?2 and the use of successive approximations. A second application of the process of ?2 is found in an extension of the theory of Schur for continued fraction expansions of functions analytic in a half-plane and of certain rational functions (?4). In ?5, a continued fraction expansion for functions analytic in R(z) >0 is obtained, and in ?6 partial fraction expansions are found for rational functions related to those discussed in ??4 and 5. 2. The real parts of the zeros of a complex polynomial. Let P(z) be the polynomial (1.1) of degree n with complex coefficients, and

On the real parts of the zeros of complex polynomials and applications to continued fraction expansions of analytic functions