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metroshane
11-13-2001, 10:40 AM
Help my buddy out..

"I have a test tomorrow and this is one of the questions. The test is open book and open notes and I am writing down all of the equations for 2-6 section Chebyshev transformers and I can't figure out the polynomial equations for a 5 and 6 section polynomial. Any help would be GREATLY appreciated.

Thanks

Pope"

JonF
11-13-2001, 11:54 AM
There are different forms, but I think these are most common:

T5 = 5x - 20x3 + 16x5

T6 = -1 + 18 x2 - 48x4 + 32x6

x5 = (10T1 + 5T3 + T5)/16

x6 = (10T0 + 15T2 + 6T4 + T6)/32

Achernar
11-13-2001, 12:19 PM
The answer to your question is about three-fifths of the way down this MathWorld page (http://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html). It just confirms what JonF said, but I wanted an excuse to plug the site.

Those are Chebyshev Polynomials of the First Kind. For Chebyshev Polynomials of the Second Kind, look three-fifths of the way down this page (http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html).

KarlGauss
11-13-2001, 12:22 PM
Eric Weisstein's World of Mathematics (http://mathworld.wolfram.com) site has been back on line for just over a week. It is a fabulous resource for any mathematical question, issue, or concept.

KarlGauss
11-13-2001, 12:31 PM
Sorry, simulpost.

JonF
11-13-2001, 03:46 PM
Yeah, but I got 'em up through order 20 here {grin}. Figured 'em out about 25 years ago and I think I've referred to 'em about three times, including this time.

Miss Creant
11-13-2001, 04:45 PM
well, sure. doesn't everyone, but I'm not gonna do your work for you

Neener neener neener

Achernar
11-13-2001, 05:32 PM
1 - 200x2 + 6600x4 - 84480x6 + 549120x8 - 2050048x10 + 4659200x12 - 6553600x14 + 5570560x16 - 2621440x18 + 524288x20, right?

JonF
11-14-2001, 11:05 AM
Originally posted by Achernar
1 - 200x2 + 6600x4 - 84480x6 + 549120x8 - 2050048x10 + 4659200x12 - 6553600x14 + 5570560x16 - 2621440x18 + 524288x20, right?

I have the coefficient of x4 as 6606, otherwise I agree.

Achernar
11-14-2001, 01:21 PM
If we only disagree on one coefficient, it should be easy enough to check, right? Since Tn(1) = 1. Of course, I'd never even heard of these things until a few days ago, so I don't want to say with any certainty.