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Applying theorem arbitrary complex numbers arc of length asymptotic directions bounded region Cartwright class of functions constants A(e converges uniformly Conversely every entire Corollary D1 belongs denote the set double-sector entire function f(z finite limit-point formal power-series function of exponential functions all zeros gn(z half-lines with directions half-plane Hence f(z kcpq lemma Let f Let f(z Let R consist Let the sequence Levinson limit-function f(z LlNDWART monotonic function N. G. DE BRUIJN number of zeros Obrechkoff partial sums points of continuity Polya polynomials fn(z positive integer Proof of theorem prove R-function regular Remark represents an entire satisfy the conditions sector with aperture sequence fn(z sequence of points sequence of polynomials sequence zn smaller type suppose Szasz tending to infinity theorem 14 type of f(z vertex z—zn zero type zeros of fn(z znp runs znp—f