Re: Jacobian zeta function; Z(\phi|m)? [summary]
- To: mathgroup at smc.vnet.net
- Subject: [mg17534] Re: Jacobian zeta function; Z(\phi|m)? [summary]
- From: Jason.Wm.Mitchell at uc.edu (Jason W. Mitchell)
- Date: Fri, 14 May 1999 01:13:07 -0400
- Organization: University of Cincinnati, ECE/CS News Server
- References: <7h4h9h$eb2@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hello; In summary, the citation for the algorithm is: Bulirsch, Roland, "Numerical Calculation of Elliptic Integrals and Elliptic Functions," Numerische Mathematik 7, pp 78--90, (1965) Be sure to read the algorithm annotations and code comments carefully to find out how to calculate Z(u|m). [I missed it the first time.] The specific algorithm is Algorithm 2 on page 82. The calculation is apparently performed through a Gauss transform on the modulus; Byrd & Friedman, Handbook of Elliptic Integrals for Engineers and Scientists, 2nd Ed. rev., p 39. As with the other "Handbook Series Special Function" papers in Numer. Math., there is Algol 60 code in a procedures section for each algorithm. Thanks Victor! Reverenter, Jason