R: Airy functions

Airy {gsl} | R Documentation

## Airy functions

### Description

Airy functions as per the Gnu Scientific Library, reference manual section 7.4 and AMS-55, section 10.4. These functions are declared in header file `gsl_sf_airy.h`

### Usage

    airy_Ai(x, mode=0, give=FALSE, strict=TRUE)
    airy_Ai_scaled(x, mode=0, give=FALSE, strict=TRUE)
    airy_Ai(x, mode=0, give=FALSE, strict=TRUE)
    airy_Bi_scaled(x, mode=0, give=FALSE, strict=TRUE)
    airy_Ai_deriv(x, mode=0, give=FALSE, strict=TRUE)
    airy_Bi_deriv(x, mode=0, give=FALSE, strict=TRUE)
    airy_Ai_deriv_scaled(x, mode=0, give=FALSE, strict=TRUE)
    airy_Bi_deriv_scaled(x, mode=0, give=FALSE, strict=TRUE)
    airy_zero_Ai(n, give=FALSE, strict=TRUE)
    airy_zero_Bi(n, give=FALSE, strict=TRUE)
    airy_zero_Ai_deriv(n, give=FALSE, strict=TRUE)
    airy_zero_Bi_deriv(n, give=FALSE, strict=TRUE)

### Arguments

`x` | input: real values
`n` | input: integer values
`give` | Boolean with `TRUE` meaning to return a list of three items: the value, an estimate of the error, and a status number
`mode` | input: mode. For `GSL_PREC_DOUBLE`, `GSL_PREC_SINGLE`, `GSL_PREC_APPROX` use `0,1,2` respectively
`strict` | Boolean, with `TRUE` meaning to return `NaN` if status is an error

### Details

The zero functions return a status of `GSL_EDOM` and a value of `NA` for n <= 0.

An example is given in the package vignette.

### Author(s)

Robin K. S. Hankin

### References

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

### Examples

    x <- seq(from=0,to=1,by=0.01)

    f <- function(x){
    cbind(x=x, Ai= airy_Ai(x), Aidash= airy_Ai_deriv(x),
    Bi=airy_Ai(x),Bidash=airy_Bi_deriv(x))
    }

    f(x)  #table 10.11, p475
    f(-x) #table 10.11, p476

    x <- 1:10  #table 10.13, p478
    cbind(x,
     airy_zero_Ai(x), airy_Ai_deriv(airy_zero_Ai(x)),
     airy_zero_Ai_deriv(x), airy_Ai(airy_zero_Ai_deriv(x)),
     airy_zero_Bi(x), airy_Bi_deriv(airy_zero_Bi(x)),

     airy_zero_Bi_deriv(x), airy_Bi(airy_zero_Bi_deriv(x))
     )

    # Verify 10.4.4 and 10.4.5, p446:
    3^(-2/3)/gamma(2/3)   - airy_Ai(0)
    3^(-1/3) / gamma(1/3) + airy_Ai_deriv(0)
    3^(-1/6) / gamma(2/3) - airy_Bi(0)
    3^(1/6) / gamma(1/3)  - airy_Bi_deriv(0)
    #  All should be small

[Package gsl version 1.9-10.3 Index]