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m-Dimensional Schlömilch Series

Published online by Cambridge University Press:  20 November 2018

Allen R. Miller
Allen R. Miller*
Affiliation:
Department of Mathematics, George Washington University, Washington, DC 20052, U.S.A.
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Abstract

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By using the principle of mathematical induction a simple algebraic formula is derived for an m-dimensional Schlömilch series. The result yields a countably infinite number of representations for null-functions on increasingly larger open intervals.

Keywords

33C10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 3 , 01 September 1995 , pp. 347 - 351
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Watson, G. N., A Treatise on the Theory ofBessel Functions, Cambridge University Press, Cambridge, 1962.Google Scholar
2. Henkel, M. and Weston, R. A., Problem 92-11*: On alternating multiple sums, SIAM Rev. 35(1993), 497– 500.Google Scholar
3. Miller, A. R., On certain two-dimensional Schlômilch series, J. Physics, A. to appearGoogle Scholar
4. Grosjean, C. C., Solving some problems posed in the SIAM Review II, Simon Stevin, to appear.Google Scholar
5. Henkel, M. and Weston, R. A., Universal amplitudes infinite-size scaling: the antiperiodic 3D spherical model, J. Phys. A 25(1992), L207–L211.Google Scholar
6. Allen, S. and Pathria, R. K., On the conjectures of Henkel and Weston, J. Phys. A 26(1993), 5173–5176.Google Scholar
7. McCoy, N. H., Introduction to Modern Algebra, Allyn and Bacon, Boston, 1960.Google Scholar
8. Exton, H., Multiple Hypergeometric Functions and Applications, Ellis Horwood, Chichester, 1976.Google Scholar
9. Magnus, W., Oberhettinger, F. and Soni, R. P., Formulas and Theorems for the Special Functions of Mathematical Physics, Springer-Verlag, New York, 1966.Google Scholar
10. Allen, S. and Pathria, R. K., Analytical evaluation of a class of phase-modulated lattice sums, J. Math. Phys. 34(1993), 1497–1507.Google Scholar
11. Ortner, N. and Wagner, P., Fundamental solution of hyperbolic differential operators and the Poisson summation formula, Integral Transforms and Special Functions 1(1993), 183—196.Google Scholar