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Hypergeometric functions










The hypergeometric function 2F1 is used in [Battin's](http://www.worldcat.org/oclc/839826772) method solving the Lambert problem, the twopoint boundary value problem for orbital motion. The derivative (see [Wolfram](http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric2F1/20/01/05/)) is helpful when solving using Newton's method.






(defun hypergeometricandderivative (z)



"The hypergeometric function F(3,1;5/2;z), (7.47), and its derivative dF/dz (7.49)."



(declare (optimize (speed 3) (debug 0) (safety 0)))



(declare (doublefloat z))



(values



(gsl:hypergeometric2F1 3.0 1.0 2.5 z)



(* 6/5 (gsl:hypergeometric2F1 4.0 2.0 3.5 z)))) 