hyperg2F1_vec {Repitools} | R Documentation

## Gaussian hypergeometric function for vectorial arguments

### Description

Computes the value of the Gaussian hypergeometric function 2_F_1 as defined in Abramowitz and Stegun (1972, page 558), i.e. for |z| < 1 and c > b > 0 using the Cephes library.

### Usage

    hyperg2F1_vec(a,b,c,z)

### Arguments

`a` | (Vectorial) parameter a.
`b` | parameter b (of same length as a)
`c` | parameter c (of same length as a)
`z` | parameter z (of same length as a)

### Details

The function is in particular efficient for vectorial arguments as the loop is shifted to `C`. Note: If vectorial arguments are provided, all arguments need to be of the same length.

### Value

The value of the Gaussian hypergeometric function F(a,b,c,z) for c > b > 0 and |z| < 1.

### Author(s)

Andrea Riebler and Daniel Sabanes Bove

### References

Abramowitz and Stegun 1972. _Handbook of mathematical functions with formulas, graphs and mathematical tables_. New York: Dowver Publications.

www.netlib.org/cephes/

### See Also

package `hypergeo` or `BMS`.

### Examples

        hyperg2F1_vec(-10.34,2.05,3.05,0.1725)
        hyperg2F1_vec(30,1,20,.8) # returns about 165.8197
        hyperg2F1_vec(30,10,20,0) # returns one
        hyperg2F1_vec(10,15,20,-0.1) # returns about 0.4872972

        hyperg2F1_vec(c(-10.34, 30, 10), c(2.05, 1, 10), c(3.05, 20, 20),
            c(0.1725, 0.8, 0))
        hyperg2F1_vec(a=1.2+1:10/10, b=rep(1.4,10), c=rep(1.665,10), z=rep(.3,10))

[Package Repitools version 1.26.0 Index]