Re: NEC-LIST: Symbolic evaluation of integrals

At 09/01/2002 20.20, D. B. Miron wrote:
>Happy New Year to you Malcolm,
>
>I assume you've looked in the big Russian compilation, by Gradsteyn and
>Ridzhykh, so I won't. I did look in Pierce and Foster's "A Short Table of
>Integbrals", 4th ed., for related forms. There's no help even in the
>definite integrals.
>
>It occurs to me that
>d(exp(-jkr))/dx = d((-jkr))/dr dr/dx
>=-jk exp(-jkr) dr/dx = -jk exp(-jkr) x/r = -jk d( I_a.)/dx
>so
>I_a=exp(-jkr)/(-jk).
>
>Am I missing something here?

The integral I_a contains x^2, which is even, not x, which is odd.

However, for likely integrals, with x^2 replaced by (cos x) or by (x sin
x ) a " closed " form can be found. I' ve used them to compute mutual
coupling between slots.

Details can be found on RWP King: theory of linear antennas, p. 94-97 for
the former and on my paper IEEE TRans Antennas Propag., nov 87, p 1289.

Hoping that this will help

Giuseppe Mazzarella

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Prof. Giuseppe MAZZARELLA, Ph. D. Senior Member, IEEE

Dip. Ing. Elettrica Elettronica Univ. di Cagliari
Piazza d'Armi
09123 CAGLIARI ITALY

Ph. + 39 070 675 5884 Fax + 39 070 675 5900

E-mail mazzarella_at_diee.unica.it

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