Introduction to the Theory of Divergent SeriesDepartment of Mathematics, Graduate School of Arts and Sciences, University of Cincinnati, 1952 - Mathematics - 81 pages |
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Abel summable absolutely convergent arithmetic means Bo(t Bo(x Borel's bounded Cauchy product Cauchy's Criterion chapter circle CnV+1 completes the proof consider defined divergent EULER SUMMABILITY exists finite formula Fourier series function f(x Given Hardy's theorem Hence Hölder Hölder means Hölder's inequality imply convergence Inasmuch infinite integral Landau's theorem lemma lim sn limit linear method of arithmetic monotonically necessary and sufficient necessary condition non-negative nt dt On+v partial sums power series prove the theorem r+p+1 regular method S₂ sequence sn sequence-to-sequence transform series belong series converges strongly summable sufficient condition summability method taken arbitrarily Tauber's theorem Tauberian condition Tauberian theorems theorem 3.4 triangular matrix triangular matrix transform write Y-method zero Π Π Σ Σ