Sviluppi in serie degli integrali ellittici, Volume 2, Part 4. Front Cover. Brigitte Radon. Accademia Nazionale dei Lincei, – Elliptic functions – 40 pages. 5th edition, Jeffrey, A. (ed.), Academic Press, New York () Radon, B.: Sviluppi in serie degli integrali ellittici. Atti Accad. Naz. Lincei, Mem., Cl. Sci. Fis. Mat. Un Sistema d’integrali Ellittici. Front Cover. Bibliographic information. QR code for Un Sistema d’integrali Ellittici. Title, Un Sistema d’integrali Ellittici.
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Hayward and James P. MR  Paul F.
EUDML | Congruenze per integrali ellittici
I was trying to see the physical meaning of the approximation. I am not sure to really answer the question here; so, please, forgive me if I am off topic.
I totally agree with you.
Assisted by Jeanne T. MR 29 ; MR 31 Terms of the last two pairs of series can be generated by means of the same recurrence relations, so that the coding of the whole is not longer than that for similar methods using only two pairs of series. The ones it mentions afterwards are concerned with incomplete integrals. If you want to test things like that, perhaps save yourself a bit of trouble and use O. This is indeed a good and elegant answer!
MR 28 ; MR 33 Email Required, but never shown. Claude, I’m not sure how conclusive the regression is.
Congruenze per integrali ellittici
There is no discussion about the beauty of what you wrote. MR  I.
What is interesting is that, based on the approximation you perfectly justified, the empirical model, once tuned, leads to a very good fit.
On the one hand, the points near 1 may not follow the asymptotic law. Byrd and Morris D. And even to get the higher terms without too much effort. Sign up using Facebook. I don’t really understand your notation. It’s unfortunate that that website doesn’t give a clear source for the expansion.
Series, 55, Superintendent of Documents, U.
integration – Approximation for elliptic integral of second kind – Mathematics Stack Exchange
MR 16 Any degree of accuracy can be obtained. Van de Vel Journal: Government Printing Office, Washington, D.
MR  A. Tome 2, Paris, The new series introduced are also represented in trigonometric form, and the double passage to the limitis discussed. My physics book gives the following approximation: On the series expansion method for computing incomplete elliptic integrals of the first and second kinds.