Repitools (version 1.18.0)

hyperg2F1_vec: 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)

Value

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

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.

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))