laguerre.weight {orthopolynom} | R Documentation |
This function returns the value of the weight function for the order k
Laguerre polynomial, L_n \left( x \right)
.
laguerre.weight(x)
x |
the function argument which can be a vector |
The function takes on non-zero values in the interval \left( 0,\infty \right)
. The formula
used to compute the weight function is as follows.
w\left( x \right) = e^{ - x}
The value of the weight function
Frederick Novomestky fnovomes@poly.edu
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.
###
### compute the Laguerre weight function for argument values
### between 0 and 3
x <- seq( -0, 3, .01 )
y <- laguerre.weight( x )
plot( x, y )