Geodesic
On Addition Theorems Related to Elliptic Integrals
Informatics and Automation, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 29-39

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We present formulas for the components of the Buchstaber formal group law and its exponent over $\mathbb Q[p_1,p_2,p_3,p_4]$. This leads to an addition theorem for the general elliptic integral $\int _0^x dt/R(t)$ with $R(t)=\sqrt {1+p_1t+p_2t^2+p_3t^3+p_4t^4}$. The study is motivated by Euler's addition theorem for elliptic integrals of the first kind.
Keywords: addition theorem, formal group law.
Mots-clés : complex elliptic genus 
@article{TRSPY_2019_305_a1,
     author = {Malkhaz Bakuradze and Vladimir V. Vershinin},
     title = {On {Addition} {Theorems} {Related} to {Elliptic} {Integrals}},
     journal = {Informatics and Automation},
     pages = {29--39},
     publisher = {mathdoc},
     volume = {305},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2019_305_a1/}
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Malkhaz Bakuradze; Vladimir V. Vershinin. On Addition Theorems Related to Elliptic Integrals. Informatics and Automation, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 29-39. http://geodesic.mathdoc.fr/item/TRSPY_2019_305_a1/