Re: NEC-LIST: Symbolic evaluation of integrals

Doug, Giuseppe is correct. I_a contains x^2.

Odd powers of x are straightforward.

Malcolm

----- Original Message -----
From: "Giuseppe Mazzarella" <mazzarella_at_diee.unica.it>
To: "D. B. Miron" <dbmiron_at_paulbunyan.net>; "Bibby" <bibby_at_mediaone.net>
Cc: "NEC-LIST" <nec-list_at_gweep.ca>
Sent: Wednesday, January 09, 2002 2:44 PM
Subject: 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
>
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>
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