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Topic: Numerical computation of chebyshev polynomial coefficients
Replies: 8   Last Post: Oct 19, 2000 6:29 AM

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Joe Ascoly

Posts: 23
Registered: 12/13/04
Re: Numerical computation of chebyshev polynomial coefficients
Posted: Oct 19, 2000 6:29 AM
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A reference for this topic is Abramowitz Handbook of
mathematical functions. I wrote programs that tabulate
the tables below. They seem to check with the Handbook
--
- Coefficients for the Chebyshev Polynomials tn(x)
every other one has sign reversed as tabulated in
Abramowitz - Handbook of Mathematical functions

TABLEC 6
0 1
1 -2 1
2 8 -8 1
3 -32 48 -18 1
4 128 -256 160 -32 1
5 -512 1280 -1120 400 -50 1
6 2048 -6144 6912 -3584 840 -72 1
X 6 5 4 3 2 1 0

1 TABLE 6 * show location of ROOTS
1 .000000 1.000000
2 .000000 .500000 1.000000
3 .000000 .250000 .750000 1.000000
4 .000000 .146447 .500000 .853553 1.000000
5 .000000 .095492 .345492 .654508 .904508 1.000000
6 .000000 .066987 .250000 .500000 .750000 .933013 1.0

2 TABLE 6 * show location of MAX

1 .500000
2 .146447 .853553
3 .066987 .500000 .933013
4 .038060 .308658 .691342 .961940
5 .024472 .206107 .500000 .793893 .975528
6 .017037 .146447 .370590 .629410 .853553 .982963

Evaluate polynomial T2 for x squared
Table 22.4 for T6 for x squared
x= .2 .4 .6 .8
0.354752 -119071 -0.752192 0.752192
* REF IS NBS BUL 55 EDITOR ABRAMOWITZ page 795 ch 22

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