ChapterTn

Chebyshev polynomial of the first kind.

Loading LOADSUB ALL FROM "CHEBY.HTS"

or LOADSUB FROM "MATHLIB.HTS"

Usage INTEGER N

REAL X,Y

Y=FNTn(N,X)

Description

FNTn returns the value of the Chebyshev polynomial of the first kind and order n of x, Tn(x). N must be positive or zero. Tn(x) is defined for all values of x, although it is most commonly used only with values of x between -1 and +1.

There are other, less used, types of Chebyshev polynomials defined that are not included in the Math Library. These can easily calculated from Tn(x) and Un(x) by using the following formulas:

Tn(x)

Errors

FNTn causes an HTBasic error if its arguments are not of the types listed in the USAGE section, above, or if the polynomial's absolute value would be larger than MAXREAL, the largest value representable.

See Also

Note

For n > 12, the algorithm used computes the value of Tn using a recursion from the values of T11 and T12. The computation time increases with n-11 and the computation accuracy decreases with n-11.