A one-sided summatory function
Author:
E. Y. State
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
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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, Introduction 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 https://doi.org/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 https://doi.org/10.1007/BF02401755 ---, Vorlesungen über Differenzenrechnung, Springer-Verlag, Berlin, 1924; reprinted, Chelsea, New York, 1954.
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Additional Information
Keywords:
One-sided series,
zeta function,
meromorphic function
Article copyright:
© Copyright 1976
American Mathematical Society
