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2012-02-20
Electric and Magnetic Field Problems with Periodic Circular Cylindrical Symmetry and Their Connection with a Novel Geometrical Interpretation of the Algebraic Operation an±Bn
By
Progress In Electromagnetics Research M, Vol. 23, 249-262, 2012
Abstract
This paper deals with the evaluation of the electric and magnetic field generated by a set of N periodically distributed filamentary conductors, in a circular arrangement. The results obtained lead to the computation of a continuous product of distances. In close connection with the computation of such a continuous product, the general problem of the factorization of a sum or difference of two powers, aN±bN, where a and b are positive real numbers and N a positive integer, is addressed.
Citation
Jose Antonio Marinho Brandao Faria, "Electric and Magnetic Field Problems with Periodic Circular Cylindrical Symmetry and Their Connection with a Novel Geometrical Interpretation of the Algebraic Operation an±Bn," Progress In Electromagnetics Research M, Vol. 23, 249-262, 2012.
doi:10.2528/PIERM11122203
References

1. Euler, L., Elements of Algebra, 2nd edition, Vol. 1, J. Johnson & Co, London, UK, 1810.

2. Diananda, P., "On integers expressible as a sum of two powers," Proc. Japan Acad., Vol. 43, 417-419, 1967.
doi:10.3792/pja/1195521558

3. Penney, D., "Multiplication relation for series of initial kth powers," Amer. Math. Monthly, Vol. 92, 729-731, 1985.
doi:10.2307/2323229

4. Gessel, I., "A formula for power series," Amer. Math. Monthly, Vol. 95, 961-962, 1988.
doi:10.2307/2322404

5. Owes, R., "Series of powers of integers," Math. Magazine, Vol. 65, 38-40, 1992.
doi:10.2307/2691359

6. Tuenter, H., "The Frobenius problem, sums of powers of integers, and recurrence for the Bernoulli numbers," J. Number Theory, Vol. 117, 376-386, 2006.
doi:10.1016/j.jnt.2005.06.015

7. Shirali, S., "On sums of powers of integers," Resonance, Vol. 12, 27-43, 2007.
doi:10.1007/s12045-007-0071-9

8. Gluck, F., "Axysymmetric electric field calculation with zonal harmonic expansion," Progress In Electromagnetics Research B, Vol. 32, 319-350, 2011.
doi:10.2528/PIERB11042106

9. Gluck, F., "Axysymmetric magnetic field calculation with zonal harmonic expansion," Progress In Electromagnetics Research B, Vol. 32, 351-388, 2011.
doi:10.2528/PIERB11042108

10. Faria, J., V. Machado, and D. van Dommelen, "Comparison of zeroth-order and harmonic expansion calculation of the electrostatic parameters of three-conductor bundles," Electric Power Systems Research, Vol. 81, 488-494, 2011.
doi:10.1016/j.epsr.2010.10.016

11. Machado, V., M. Pedro, J. Faria, and D. van Dommelen, "Magnetic field analysis of three-conductor bundles in flat and triangular configurations with the inclusion of proximity and skin effects," Electric Power Systems Research, Vol. 81, 2005-2014, 2011.
doi:10.1016/j.epsr.2011.06.010

12. Solymar, L., Lectures on Electromagnetic Theory, Oxford University Press, Oxford, UK, 1984.

13. Faria, J., Electromagnetic Foundations of Electrical Engineering, Wiley, Chichester, UK, 2008.
doi:10.1002/9780470697498

14. Spiegel, M. and L. Rapun, Mathematical Handbook of Formulas and Tables, McGraw-Hill, New York, USA, 1970.

15. Gonzalez-Morales, M. J., R. Mahillo-Isla, E. Gago-Ribas, and C. Dehesa-Martinez, "Complex polar coordinates in electromagnetics," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 2-3, 389-398, 2011.
doi:10.1163/156939311794362795

16. Wiles, A., "Modular elliptic curves and Fermat's last theorem," Annals of Mathematics, Vol. 141, 443-551, 1995.
doi:10.2307/2118559

17. Barros, M., "Computation of line parameters," European EMTP Short Course, Belgium, Jul.-Aug. 1984.