# jacobi.p.weight: Weight function for the Jacobi polynomial

Description Usage Arguments Details Value Author(s) References Examples

### Description

This function returns the value of the weight function for the order k Jacobi polynomial, P_k^{≤ft( {α ,β } \right)} ≤ft( x \right).

### Usage

 1 jacobi.p.weight(x,alpha,beta) 

### Arguments

 x the function argument which can be a vector alpha the first polynomial parameter beta the second polynomial parameter

### Details

The function takes on non-zero values in the interval ≤ft( -1,1 \right) . The formula used to compute the weight function is as follows.

w≤ft( x \right) = ≤ft( {1 - x} \right)^α \;≤ft( {1 + x} \right)^β

### 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

 1 2 3 4 5 6 ### ### compute the Jacobi P weight function for argument values ### between -1 and 1 ### x <- seq( -1, 1, .01 ) y <- jacobi.p.weight( x, 2, 2 ) 

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