Elliptic Integrals
The paper that Wayne Bell is using dates from 1962, so it’s not surprising that Professor Robert Israel found its format for elliptic integrals differs from those of Maple and Mathematika. Indeed, it differs from those of Professor LM Milne-Thompson (circa 1960) in A&S chapter 17. It belongs to an earlier era, though - according to an antique textbook of mine (circa 1930s) - the format would have been reversed, i.e. F(k,beta) and E(k,beta).
It’s curious that Maple adopted a format, resembling but differing from that of A&S. Does anyone know the reason?
May I suggest to Wayne Bell that, if he has not already done so, he should review the many papers on the subject that have been published since 1962. He might also find some useful material in naval architecture and design codes for submarines and unmanned underwater vehicles. Essentially, these are thick tubes reinforced by deep ring girders and subjected to very great hydrostatic pressures.
J. Tarr
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