| hermite.h.weight {orthopolynom} | R Documentation |
Weight function for the Hermite polynomial
Description
This function returns the value of the weight function for the order k
Hermite polynomial, H_k \left( x \right).
Usage
hermite.h.weight(x)
Arguments
x |
the function argument which can be a vector |
Details
The function takes on non-zero values in the interval \left( -\infty,\infty \right) . The
formula used to compute the weight function.
w\left( x \right) = \exp \left( { - x^2 } \right)
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 Hermite weight function for argument values
### between -3 and 3
x <- seq( -3, 3, .01 )
y <- hermite.h.weight( x )
plot( x, y )