The General Theory of Dirichlet's Series
This classic work by two distinguished mathematicians explains theory and formulas behind Dirichlet's series and offers first systematic account of Riesz's theory of 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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abscissa absolute convergence apply argument associated Bohr Chapman choose complete concerning condition consider constant contains deduce deﬁned deﬁnitions denote depends Dirichlet’s series Dirichletschen easily equation established evident example expression extended ﬁnd ﬁnite ﬁrst follows formula function Further generalisation give given greater half-plane Hardy Hence holds important increase inequalities inﬁnity integral interesting involves Journal Knopp Landau Lemma less limit Littlewood Math mean value theorem methods multiplication necessary observe obtain obviously occurs once ordinary Dirichlet’s series particular positive possible power series proof prove reader refer region regular Reihen relation remains replaced represents result Riesz sÚries series is convergent series is summable shown similar simple substitute summation suppose tends term Theorem 17 Theorems 23 theory throughout true typical means Uber values write zero