A one-sided summatory function
HTML articles powered by AMS MathViewer
- by E. Y. State
- Proc. Amer. Math. Soc. 60 (1976), 134-138
- DOI: https://doi.org/10.1090/S0002-9939-1976-0422629-3
- PDF | 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, Mass., 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.
Bibliographic 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