The General Theory of Dirichlet's Series
This classic work, written by two of the 20th century's most distinguished mathematicians, explains the theory and formulas behind Dirichlet's series and offers the first systematic account of Riesz's theory of the summation of series by typical means. 1915 edition.
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The formula for the sum of the coefficients of
The summation of series by typical means
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Abel's theorem absolutely convergent Acta Math ambn apply argument arithmetic means Biesz Bohr Borel's Bromwich Cauchy's Theorem Cesaro's Chapman circle of convergence coefficient Comptes Rendus consider deduce defined Dirichletscher Reihen edition equation Felix Klein finite order follows from Theorem formula Fourier's series function G. H. Hardy Hardy and Littlewood Hence important theorem inequalities Infinite series infinity integral Knopp Landau Lemma limit Lindelof Lindelof's Theorem line of convergence logarithmic means Lond mean value theorem methods of summation obtain ordinary Dirichlet's series positive number positive values power series Proc proof of Theorem proves the theorem region of convergence regular Rendiconti di Palermo result Riesz Schnee second kind series is convergent series is summable series is uniformly suppose tends to zero term Theorem 17 Theorem 41 Theorems 23 theory of Dirichlet's tjber typical means Unabridged republication uniformly convergent uniformly summable vergence