F1 {tolerance}

Appell's F1 Hypergeometric Function

Description

The Appell function of the first kind, which is a two variable extension of the hypergeometric distribution.

Usage

F1(a, b, b.prime, c, x, y, ...)

Arguments

a, b, b.prime, c

Appropriate parameters for this function.

x, y

The inputted values to evaluate this function such that each is less than 1 in absolute value.

...

Additional arguments passed to the integrate function.

Value

F1 returns the simple integral result for the Appell function of the first kind with the arguments specified above.

Note

This function is solved by using a simple integral representation for real numbers. While all four of the Appell functions can be extended to the complex plane, this is not an option for this code.

References

Bailey, W. N. (1935), Generalised Hypergeometric Series, Cambridge University Press.

See Also

DiffProp, integrate

Examples

 
## Sample calculation.

F1(a = 3, b = 4, b.prime = 5, c = 13, x = 0.2, y = 0.4)