Efficient and Accurate Approximation of Infinite Series Summation Using Asymptotic Approximation and Fast Convergent Series

doi:10.2528/PIERM11100810

PIER M
Progress In Electromagnetics Research M	ISSN: 1937-8726

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EFFICIENT AND ACCURATE APPROXIMATION OF INFINITE SERIES SUMMATION USING ASYMPTOTIC APPROXIMATION AND FAST CONVERGENT SERIES

By S. Jain and J.-M. Song

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Abstract:
We present an approach for very quick and accurate approximation of infinite series summation arising in electromagnetic problems. This approach is based on using asymptotic expansions of the arguments and the use of fast convergent series to accelerate the convergence of each term. It has been validated by obtaining very accurate solution for propagation constant for shielded microstrip lines using spectral domain approach (SDA). In the spectral domain analysis of shielded microstrip lines, the elements of the Galerkin matrix are summations of infinite series of product of Bessel functions and Green's function. The infinite summation is accelerated by leading term extraction using asymptotic expansions for the Bessel function and the Green's function, and the summation of the leading terms is carried out using the fast convergent series.

Citation:
S. Jain and J.-M. Song, "Efficient and accurate approximation of infinite series summation using asymptotic approximation and fast convergent series," Progress In Electromagnetics Research M, Vol. 22, 191-203, 2012.
doi:10.2528/PIERM11100810
http://www.jpier.org/pierm/pier.php?paper=11100810

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