# Gegenbauer: Gegenbauer functions In gsl: Wrapper for the Gnu Scientific Library

 Gegenbauer R Documentation

## 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)

```

gsl documentation built on Feb. 16, 2023, 10:32 p.m.