The hypergeometric function 2F1 is used in [Battin's](http://www.worldcat.org/oclc/839826772) method solving the Lambert problem, the two-point boundary value problem for orbital motion. The derivative with respect to the final argument (see [Wolfram](http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric2F1/20/01/05/)) is helpful when solving using Newton's method.
(set-reader-in-file)
(defun hypergeometric-and-derivative (z)
"The hypergeometric function F(3,1;5/2;z), (7.47), and its derivative dF/dz (7.49)."