Abstract. In 1914 Pólya raised the problem of classifying the entire functions which together with all their derivatives have only real zeros. In earlier work Hellerstein and Williamson settled this problem for entire functions which are real on the real axis. We complete the classification in all cases and show that it is sufficient to consider the function and its first two derivatives.

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Abstract. Based on properties of the hypergeometric series 2 F 1 ( ; z), we develop a theory of elliptic functions that shares many striking similarities with the classical Jacobian elliptic functions.

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