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orthopoly

  

T

  

Chebyshev polynomial (of the first kind)

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

T(n, x)

Parameters

n

-

non-negative integer

x

-

algebraic expression

Description

• 

The T(n, x) function computes the nth Chebyshev polynomial of the first kind evaluated at x.

• 

These polynomials are orthogonal on the interval (1,1) with respect to the weight function wx=1x2+1. They satisfy:

−11wtTm,tTn,tⅆt=0nmπn=mandm=0π2n=mandm0

• 

Chebyshev polynomials of the first kind satisfy the following recurrence relation:

T0,x=1,

T1,x=x,

Tn,x=2xTn1,xTn2,x,for n > 1.

Examples

withorthopoly:

T2,x

2x21

(1)

T3,x

4x33x

(2)

T50,13

203160711589551869872313717897987691852588770249

(3)

See Also

ChebyshevT

LambertW

numapprox[chebyshev]

 


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