| chebyshev.t.weight {orthopolynom} | R Documentation |
Weight function for the Chebyshev polynomial
Description
This function returns the value of the weight function for the order k Chebyshev polynomial
of the first kind, T_k \left( x \right) .
Usage
chebyshev.t.weight(x)
Arguments
x |
the function argument which can be a vector |
Details
The function takes on non-zero values in the interval \left( -1,1 \right) . The formula
used to compute the weight function is as follows.
w\left( x \right) = \frac{1}{{\sqrt {1 - x^2 } }}
Value
The value of the weight function.
Author(s)
Frederick Novomestky fnovomes@poly.edu
References
Abramowitz, M. and I. A. Stegun, 1968. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., New York.
Courant, R., and D. Hilbert, 1989. Methods of Mathematical Physics, John Wiley, New York, NY.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992. Numerical Recipes in C, Cambridge University Press, Cambridge, U.K.
Szego, G., 1939. Orthogonal Polynomials, 23, American Mathematical Society Colloquium Publications, Providence, RI.
Examples
###
### compute the T Chebyshev function for argument values between -2 and 2
x <- seq( -1, 1, .01 )
y <- chebyshev.t.weight( x )
plot( x, y )