Some integrals involving squares of Bessel functions and generalized Legendre polynomials

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E. Matagne

Abstract

This paper develops new integral formulas intended for detailed studies of electromagnetics normal modes in spherical and spherical annular cavities.

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How to Cite
Matagne, E. (2022). Some integrals involving squares of Bessel functions and generalized Legendre polynomials. Advanced Electromagnetics, 11(4), 80–83. https://doi.org/10.7716/aem.v11i4.1946
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Research Articles

References

REFERENCES

R.A. Yadav and I.D. Singh, "Normal modes and quality factors of spherical dielectric resonators: I - Shielded dielectric sphere," PRAMANA journal of physics, vol. 62, no. 6, pp. 1255-1271, June 2004.

View Article

D.W. Vogt and R. Leonhardt, "Ultra-high Q terahertz whispering-gallery modes in a silicon resonator," APL Photonics, vol. 3, 051702, 2018.

View Article

T. H. Boyer, "Quantum Electromagnetic Zero-Point Energy of a Conducting Spherical Shell and the Casimir Model for a Charged Particle," Physical Review, vol. 174, no. 5, pp. 1764-1776, October 1963.

View Article

Y. Avni and U. Leonhardt, "Casimir self-stress in dielectric sphere," Annals of Physics, vol. 395, pp. 326-340, 2018.

View Article

T. Gong, M.R. Corrado, A.R. Mahbub, C. Shelden and J.N. Munday "Recent progress in engineering the Casimir effect - application to nanophotonics, nanomechanics and chemistry," Nanophotonics, vol. 10, no. 1, pp. 523-536, 2021.

View Article

M. Abramowitz and J. A. Stegun, Handbook of Mathematical Functions, Dover Publications, INC, NY, 1965.

WolframMathWorld, Lommel's Integrals, [Online]. Available: http://mathworld.wolfram.com/LommelsIntegrals.html, Accessed on: May 8 2021.

V. G. Bagrov, V. V. Belov, V. N. Zadorozhnyi and A. Yu. Trifonov, "Methods of mathematical physics. Special Functions. Equations of Mathematical Physics.,"Tomsk Polytechnic University Publishing House, 2012.

F. Bowman, Introduction to Bessel Functions, Dover Publications, INC, NY, 1958.

T. M. Dunster, "Chapter 14 Legendre and Related Functions," in NIST Digital Library of Mathematical Functions, NIST Digital Library of Mathematical Functions [Online]. Available: http://dlmf.nist.gov/14.10, Accessed on May 8 2021.

S. N. Samaddar, "Some Integrals Involving Associated Legendre Functions," Mathematics of Computation, vol. 28, no. 125, pp. 257-263, January 1974.

View Article