E589 -- Investigatio valoris integralis ∫ (x^(m-1) dx)/(1-2(x^k)cos(θ)+x^(2k)) a termino x = 0 ad x = ∞ extensi

E589 -- Investigatio valoris integralis \(\int\! \frac{x^{m-1}\,dx}{1-2x^k\cos\theta +x^{2k}}\) a termino \(x = 0\) ad \(x = \infty\) extensi

(An investigation of the value of the integral \(\displaystyle \int\! \frac{x^{m-1}\,dx}{1-2x^k\cos\theta +x^{2k}}\), the term to be extended from \(x = 0\) to \(x = \infty\))

Summary:

According to the records, it was presented to the St. Petersburg Academy on March 2, 1775.

Publication:

Originally published in Opuscula Analytica 2, 1785, pp. 55-75
Opera Omnia: Series 1, Volume 18, pp. 190 - 208
Reprinted in Institutiones calculi integralis 4, 1794, pp. 358-378 [E589a], ed. tertia, 4, 1845, pp. 358-378 [E589b]

Documents Available:

Original Publication: E589

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