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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A one-sided summatory function
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by E. Y. State PDF
Proc. Amer. Math. Soc. 60 (1976), 134-138 Request permission

Abstract:

A method is given for summing one-sided series by employing the psi function. $\sum \nolimits _{n = 1}^\infty {{n^{ - k}}\Psi (n)}$ is evaluated in closed form when $k \geqslant 2$ is an integer.
References
    M. Abramowitz and I. A. Stegun (Editors), Handbook of mathematical functions with formulas, graphs, and mathematical tables, Nat. Bur. Standards Appl. Math. Ser., no. 55, Supt. of Documents, U.S. Gov’t. Printing Office, Wash., D.C., 1964. MR 29 #4914.
  • Einar Hille, Analytic function theory. Vol. 1, Introductions to Higher Mathematics, Ginn and Company, Boston, 1959. MR 0107692
  • D. H. Lehmer, Euler constants for arithmetical progressions, Acta Arith. 27 (1975), 125–142. MR 369233, DOI 10.4064/aa-27-1-125-142
  • N. E. Nörlund, Mémoire sur les polynomes de bernoulli, Acta Math. 43 (1922), no. 1, 121–196 (French). MR 1555176, DOI 10.1007/BF02401755
  • —, Vorlesungen über Differenzenrechnung, Springer-Verlag, Berlin, 1924; reprinted, Chelsea, New York, 1954.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 134-138
  • MSC: Primary 30A86
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0422629-3
  • MathSciNet review: 0422629