Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Chebyshev polynomials

.

I've done the first part using induction. The polynomials I chose were:

However, the last part is a bit tricky.

I can't see how to write this in the form

though. I know that

and

Can anyone help? (Small hints preferred) Thanks.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Chebyshev polynomials

No one?

Kurre

Member

Registered: 2006-07-18

Posts: 280

Re: Chebyshev polynomials

Cos2x+Cos3x=0
Cos2x=-Cos3x
Cos2x=Cos(pi-3x)
1)2x=3x-pi->x=pi->cosx=-1
2)2x=pi-3x->x=pi/5
looks like something is wrong with your equation...

Last edited by Kurre (2008-12-06 07:14:54)

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Chebyshev polynomials

Cos2x+Cos3x=0
Cos2x=-Cos3x
Cos2x=Cos(pi-3x)
1)2x=3x-pi->x=pi->cosx=-1
2)2x=pi-3x->x=pi/5
looks like something is wrong with your equation...

You're right.

I'm actually rather stupid.

The factor should be (x+1), in which case x = -1 does work, as we can let x = cosθ (which we have to do anyway). Also,

Thanks

The point of the question was obviously to work in the trigonometric form, as the value of phi s.t

isn't obvious.

Last edited by Daniel123 (2008-12-06 08:20:13)