## Interpolatory function theory |

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### Contents

Preface page | 1 |

The Sum of a Function | 17 |

Properties of Successive Derivatives | 32 |

Copyright | |

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a-shire absolutely convergent an+1 asymptotic periods basic series basic set Bernoulli polynomials boundary cardinal series circle of centre circle of radius coefficients complete pair continuous function converges absolutely converges uniformly defined E. T. Whittaker equal equation everywhere dense exponent of convergence finite number finite order finite region follows form a basic form a set Fourier series function g function of order given positive number Gontcharoff Hence Iff(z infinite integral or meromorphic interpolation Kakeya lemma Letf(z log+ logr maximum modulus measure zero meromorphic function Moreover Nevanlinna order less plane Polya proof properties prove radius of convergence regular result satisfies the condition satisfies the inequality series converges set of measure set of operators set of polynomials simple set standard set summable Suppose Taylor series tending to infinity than/(z Theorem Theorem 16 upper density Valiron Write