E581 -- Plenior explicatio circa comparationem quantitatum in formula integrali \(\int\! \frac{Z\,dz}{\sqrt{1+mzz+nz^4}}\) contentarum denotante \(Z\) functionem quamcunque rationalem ipsius \(zz\)
(A more complete investigation into the relationship between those quantities contained in the integral formula \(\displaystyle \int\! \frac{Z\,dz}{\sqrt{1+mzz+nz^4}}\), where \(Z\) denotes a rational function of \(zz\))
Summary:
According to the records, it was presented to the St. Petersburg Academy on August 14, 1775.
Publication:
- Originally published in Acta Academiae Scientarum Imperialis Petropolitinae 1781, 1785, pp. 3-22
- Opera Omnia: Series 1, Volume 21, pp. 39 - 56
- Reprinted in Institutiones calculi integralis 4, 1794, pp. 446-464 [E581a], ed. tertia 4, 1845, pp.446-464 [E581b]
Documents Available:
- Original Publication: E581
- Alexander Aycock has made draft translations into German and English, available online at Euler-Kreis Mainz.
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