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Proceedings of the American Mathematical Society

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A one-sided summatory function

Author: E. Y. State
Journal: Proc. Amer. Math. Soc. 60 (1976), 134-138
MSC: Primary 30A86
MathSciNet review: 0422629
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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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Keywords: One-sided series, zeta function, meromorphic function
Article copyright: © Copyright 1976 American Mathematical Society