Gegenbauer {gsl}

Gegenbauer functions

Description

Gegenbauer functions as per the Gnu Scientific Library reference manual section 7.20, and AMS-55, chapter 22. These functions are declared in header file gsl_sf_gegenbauer.h

Usage

gegenpoly_1(lambda, x, give=FALSE,strict=TRUE)
gegenpoly_2(lambda, x, give=FALSE,strict=TRUE)
gegenpoly_3(lambda, x, give=FALSE,strict=TRUE)
gegenpoly_n(n,lambda, x, give=FALSE,strict=TRUE)
gegenpoly_array(nmax,lambda, x, give=FALSE,strict=TRUE)

Arguments

lambda, x

input: real values

n, nmax

input: integer value

give

Boolean with TRUE meaning to return a list of three items: the value, an estimate of the error, and a status number

strict

Boolean, with TRUE meaning to return NaN if status is an error

Author(s)

Robin K. S. Hankin

References

https://www.gnu.org/software/gsl/

Examples

x <- seq(from=-1 ,to=1,len=300)
y <- gegenpoly_array(6,0.5,x)
matplot(x,t(y[-(1:2),]), xlim=c(-1,1.2),ylim=c(-0.5,1.5),
       type="l",xaxt="n",yaxt="n",bty="n",xlab="",ylab="",
       main="Figure 22.5, p777",col="black")
axis(1,pos=0)
axis(2,pos=0)


plot(x, gegenpoly_n(5,lambda=0.2, x,give=FALSE,strict=TRUE),
xlim=c(-1,1),ylim=c(-1.5,1.5),main="Figure 22.5, p777",
type="n",xaxt="n",yaxt="n",bty="n",xlab="",ylab="")
lines(x, gegenpoly_n(5,lambda=0.2, x,give=FALSE,strict=TRUE))
lines(x, gegenpoly_n(5,lambda=0.4, x,give=FALSE,strict=TRUE))
lines(x, gegenpoly_n(5,lambda=0.6, x,give=FALSE,strict=TRUE))
lines(x, gegenpoly_n(5,lambda=0.8, x,give=FALSE,strict=TRUE))
lines(x, gegenpoly_n(5,lambda=1.0, x,give=FALSE,strict=TRUE))
axis(1,pos=0)
axis(2,pos=0,las=1)