Email this article On Addition Theorems Related to Elliptic Integrals
- Authors: Bakuradze M.1, Vershinin V.V.2,3
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Affiliations:
- Faculty of Exact and Natural Sciences
- Institut Montpelliérain Alexander Grothendieck
- Sobolev Institute of Mathematics
- Issue: Vol 305, No 1 (2019)
- Pages: 22-32
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/175796
- DOI: https://doi.org/10.1134/S0081543819030027
- ID: 175796
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Abstract
We present formulas for the components of the Buchstaber formal group law and its exponent over ℚ[p1, p2, p3, p4]. This leads to an addition theorem for the general elliptic integral \(\int_0^x {dt{\rm{/}}R\left( t \right)} \) with \(R(t)=\sqrt{1+p_{1} t+p_{2} t^{2}+p_{3} t^{3}+p_{4} t^{4}}\). The study is motivated by Euler’s addition theorem for elliptic integrals of the first kind.
About the authors
Malkhaz Bakuradze
Faculty of Exact and Natural Sciences
Author for correspondence.
Email: malkhaz.bakuradze@tsu.ge
Georgia, Chavchavadze Ave. 1, Tbilisi, 0179
Vladimir V. Vershinin
Institut Montpelliérain Alexander Grothendieck; Sobolev Institute of Mathematics
Author for correspondence.
Email: vladimir.verchinine@umontpellier.fr
France, Case courrier 051, Place Eugène Bataillon, Montpellier, 34090; pr. Akademika Koptyuga 4, Novosibirsk, 630090
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