orthopolynom (version 1.0-2)

ultraspherical.weight: Weight function for the ultraspherical polynomial

Description

This function returns the value of the weight function for the order $k$ ultraspherical polynomial, $C_k^{\left( \alpha \right)} \left( x \right)$.

Usage

ultraspherical.weight(x,alpha)

Arguments

x

the function argument which can be a vector

alpha

polynomial parameter

Value

• The value of the weight function

Details

The function takes on non-zero values in the interval $\left( -1,1 \right)$.

References

Abramowitz and Stegun (1968)

Examples

x <- seq( -2, 2, .01 )
y <- ultraspherical.weight( x, 1 )