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Recently Dr. Israel responded to my request for help in extending the EllipticF function past the limit of Pi/2 for the amplitude (see topic titled Elliptic Integrals). After reviewing A&S Chapter 17, I have tried to duplicate the results using the JacobiAM function in Maple. The help page for this function indicates that there is no limit on the amplitude. The attached worksheet evaluates the form suggested by A&S, Eq. 17.4.3 and the JacobiAM function. It is interesting to note the only when the argument given to the EllipticF function is equal to the remainder of Pi/2 - beta that the two expressions are equal. I would think that the JacobiAM form is a more compact representation of EllipticF for amplitudes greater than Pi/2. Are the two functions equivalent as used in the worksheet? Your thoughts/comments are appreciated. View 4865_InvJacobi.mw on MapleNet or Download 4865_InvJacobi.mw
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