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2007-06-12
An Overview of the Watson Transformation Presented through a Simple Example
By
Progress In Electromagnetics Research, Vol. 75, 137-152, 2007
Abstract
One of the methods developed for accelerating the convergence speed of infinite series is theWatson transformation. It is a technique with an interesting theoretical background which is applied in a restricted number of cases due to its complexity. Most of the papers using this method do not extensively analyze every step of implementation. In this work we apply Watson transformation in a simple case and we focus on each aspect of the procedure.
Citation
Constantinos Valagiannopoulos , "An Overview of the Watson Transformation Presented through a Simple Example," Progress In Electromagnetics Research, Vol. 75, 137-152, 2007.
doi:10.2528/PIER07052502
http://www.jpier.org/PIER/pier.php?paper=07052502
References

1. Fikioris, G., "An application of convergence acceleration methods," IEEE Trans. Antennas Propag., Vol. 47, No. 12, 1758-1760, 1999.
doi:10.1109/8.817649

2. Scraton, R. E., "The practical use of the Euler transformation," Journal BIT Numerical Mathematics, Vol. 29, No. 2, 356-260, 2005.
doi:10.1007/BF01952689

3. Soler, F. J. P., F. D. Q. Pereira, J. P. Garc´ia, D. C. Rebenaque, and A. ´A. Melc´on, "Analysis of inductive waveguide microwave components using an alternative port treatment and efficient fast multipole," Progress In Electromagnetics Research, Vol. 68, 71-90, 2007.

4. Pereira, F. Q., F. J. P. Soler, J. P. Garcia, V. E. B. Esbert, B. G. Martinez, and A. A. Melcon, Comparison between the Kummer's transformation and Ewald's method for the evaluation of the parallel plate Green's functions, Antennas Propag. Society International Symposium 2006, 9-14, 2006.

5. Hussar, P. E. and E. M. Smith-Rowland, "An asymptotic solution for boundary layer fields near a convex impedance surface," Journal of Electromagnetic Waves and Applications, Vol. 16, No. 2, 185-208, 2002.

6. Shim, J. and H.-T. Kim, "Dominance of creeping wave modes of backscattered field from a conducting sphere with dielectric coating," Progress In Electromagnetics Research, Vol. 21, 293-306, 1999.
doi:10.2528/PIER98082503

7. Andropov, I. V. and D. Bouche, "Asymptotics of creeping waves in a degenerated case of matrix impedance," Progress In Electromagnetics Research, Vol. 59, 215-230, 2006.
doi:10.2528/PIER05093001

8. Watson, G. N., The diffraction of electric waves by the earth, Proceedings of the Royal Society of London, Vol. 95, No. 666, 83-99, 1918.

9. Uberall, H., "Acoustic scattering from elastic cylinders and spheres: surface waves (Watson transform) and transitted waves," Diffusion et Diffraction, Vol. 2, No. 5, 353-387, 1985.

10. Rosengren, H., "Karlsson-Minton type hypergeometric functions on the root system Cn," Journal of Mathematical Analysis and Applications, Vol. 281, No. 1, 332-345, 2003.

11. Fisher, E., "On the watson transformation," Communications on Pure and Applied Mathematics, Vol. XIX, 287-297, 1966.
doi:10.1002/cpa.3160190304

12. Pumplin, J., "Application of Sommerfeld-Watson transformation to an electrostatics problem," American Journal of Physics, Vol. 37, No. 7, 737-739, 1969.
doi:10.1119/1.1975793

13. Okhmatovski, V. I. and A. C. Cangellaris, "Efficient calculation of the electromagnetic dyadic Green's function in spherical layered media," IEEE Trans. Antennas Propag., Vol. 51, No. 12, 3209-3220, 2003.
doi:10.1109/TAP.2003.820952

14. Wang, H.-L., Q. Wu, X.-J. He, and L.-W. Li, Computation of wave scattering problems from a spheric body: derivation of the new Sommerfeld-Watson transformation, Progress In Electromagnetics Research Symposium 2005, 22-26, 2005.

15. Valagiannopoulos, C. A., "Single-series solution to the radiation of loop antenna in the presence of a conducting sphere," Progress In Electromagnetics Research, Vol. 71, 277-294, 2007.
doi:10.2528/PIER07030803

16. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Washington D.C., 1970.