Geodesic
On algorithms for calculating complete elliptic integrals
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 5-16 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Methods for calculating complete elliptic integrals of the first and second kind and their implementation in the MathPartner computer algebra system are considered. 
@article{ZNSL_2022_517_a0,
     author = {S. Adlaj and G. I. Malashonok and K. Yu. Malyshev and A. V. Seliverstov and F. G. Uskov},
     title = {On algorithms for calculating complete elliptic integrals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--16},
     year = {2022},
     volume = {517},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a0/}
}
TY  - JOUR
AU  - S. Adlaj
AU  - G. I. Malashonok
AU  - K. Yu. Malyshev
AU  - A. V. Seliverstov
AU  - F. G. Uskov
TI  - On algorithms for calculating complete elliptic integrals
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2022
SP  - 5
EP  - 16
VL  - 517
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a0/
LA  - ru
ID  - ZNSL_2022_517_a0
ER  - 
%0 Journal Article
%A S. Adlaj
%A G. I. Malashonok
%A K. Yu. Malyshev
%A A. V. Seliverstov
%A F. G. Uskov
%T On algorithms for calculating complete elliptic integrals
%J Zapiski Nauchnykh Seminarov POMI
%D 2022
%P 5-16
%V 517
%U http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a0/
%G ru
%F ZNSL_2022_517_a0
S. Adlaj; G. I. Malashonok; K. Yu. Malyshev; A. V. Seliverstov; F. G. Uskov. On algorithms for calculating complete elliptic integrals. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 5-16. http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a0/

[1] V. F. Edneral, “In memory of Vladimir Gerdt”, Discrete and Continuous Models and Applied Computational Science, 29:4 (2021), 306–336 | DOI | MR

[2] G. I. Malaschonok, “MathPartner computer algebra”, Programming and Computer Software, 43:2 (2017), 112–118 | DOI | MR

[3] G. I. Malaschonok, A. V. Seliverstov, “Calculation of integrals in MathPartner”, Discrete and Continuous Models and Applied Computational Science, 29:4 (2021), 337–346 | DOI

[4] M. D. Malykh, L. A. Sevastianov, Yu Ying, “On symbolic integration of algebraic functions”, J. Symbolic Computation, 104 (2021), 563–579 | DOI | MR

[5] A. V. Seliverstov, “Heuristic algorithms for recognition of some cubic hypersurfaces”, Programming and Computer Software, 47 (2021), 50–55 | DOI | MR

[6] R. Reynolds, A. Stauffer, “Definite integral of logarithmic functions and powers in terms of the lerch function”, Ural Math. J., 7:1 (2021), 96–101 | DOI | MR

[7] S. Adlaj, “An eloquent formula for the perimeter of an ellipse”, Notices Amer. Math. Soc., 59:8 (2012), 1094–1099 | DOI | MR

[8] S. F. Adlaj, “Elliptic integrals, functions, curves and polynomials”, Computer Assisted Mathematics, 2019, no. 1, 3–8

[9] J. M. Borwein, P. B. Borwein, “The arithmetic-geometric mean and fast computation of elementary functions”, SIAM Review, 26:3 (1984), 351–366 | DOI | MR

[10] B. Sury, “The arithmetico-geometric mean of Gauss”, Resonance, 5:8 (2000), 72–83 | DOI

[11] S. Adlaj, “An analytic unifying formula of oscillatory and rotary motion of a simple pendulum”, Proceedings of International Conference “Geometry, Integrability, Mechanics and Quantization” (Varna, Bulgaria, June 6–11, 2014), Avangard Prima, Sofia, 2015, 160–171

[12] S. Adlai, Ravnovesie niti v lineinom parallelnom pole sil, LAP LAMBERT, Mauritius, 2018

[13] S. Adlaj, “An explicit procedure for calculating the perimeter of an ellipse”, 22nd Workshop on Computer Algebra in memory of Professor Vladimir Gerdt (Dubna, Russia, 2021), 5–6

[14] F. Lamarche, C. Leroy, “Evaluation of the volume of intersection of a sphere with a cylinder by elliptic integrals”, Computer Physics Communications, 59:2 (1990), 359–369 | DOI | MR

[15] N. J. Mariani, G. D. Mazza, O. M. Martinez, G. F. Barreto, “Evaluation of radial voidage profiles in packed beds of low-aspect ratios”, Canadian J. Chemical Engineer., 78:6 (2000), 1133–1137 | DOI

[16] B.-X. Xu, Y. Gao, M.-Z. Wang, “Particle packing and the mean theory”, Physics Letters A, 377:3–4 (2013), 145–147

[17] E. Agol, R. Luger, and D. Foreman-Mackey, “Analytic Planetary Transit Light Curves and Derivatives for Stars with Polynomial Limb Darkening”, Astronom. J., 159:3 (2020), 123–159 | DOI

[18] R. H. Good, “Elliptic integrals, the forgotten functions”, European J. Phys., 22 (2001), 119–126 | DOI | MR

[19] B. M. Budak, A. A. Samarskii, A. N. Tikhonov, Sbornik zadach po matematicheskoi fizike, 4-e izd., ispr., Fizmatlit, M., 2004, 688 pp. | MR

[20] F. Lamarche, A calculation of the exact field near a loop of current, http://frogolandia.50megs.com/MathDemos.html

[21] Yu. P. Ivochkin, D. A. Vinogradov, I. O. Teplyakov, “Chislennyi raschet magnitnogo polya s ispolzovaniem tekhnologii CUDA primenitelno k modelirovaniyu elektrovikhrevykh techenii”, Matematicheskoe i programmnoe obespechenie sistem v promyshlennoi i sotsialnoi sferakh, 2015, no. 2, 13–18

[22] I. Teplyakov, D. Vinogradov, Y. Ivochkin, “Experimental study of the velocity of the electrovortex flow of In-Ga-Sn in hemispherical geometry”, Metals, 11:11 (2021), 1806 | DOI

[23] J. Landen, “An investigation of a general theorem for finding the length of any arc of any conic hyperbola by means of two elliptic arcs, with some other new and useful theorems deduced therefrom”, Phil. Trans., LXV (1775), 283–289

[24] A. Cayley, “Note on Landen's theorem”, The Proceedings of the London Mathematical Society, XIII (1882), 47–48 | MR

[25] S. B. Gashkov, I. S. Sergeev, “Umnozhenie”, Chebyshevskii sb., 21:1 (2020), 101–134 | MR

[26] É. Galois, “Analyse algébrique. Démonstration d'un théorème sur les fractions continues périodiques”, Annalles de Mathématiques pures et appliquées, 19 (1828–1829), 294–301 | MR

[27] V. S. Vladimirov, Equations of Mathematical Physics, Marcel Dekker, New York, 1971 | MR

[28] F. Lamarche, Modified Arithmetic-Geometric Mean, (Data obrascheniya 27 iyulya 2022) https://math.stackexchange.com/questions/391382/modified-arithmetic-geometric-mean

[29] W. Chu, “Ramanujan-like formulae for $\pi$ and $1/\pi$ via Gould–Hsu inverse series relations”, Ramanujan J., 56 (2021), 1007–1027 | DOI | MR

[30] J. Guillera, “A method for proving Ramanujan's series for $1/\pi$”, Ramanujan J., 52 (2020), 421–431 | DOI | MR

[31] D. Takahashi, “On the computation and verification of $\pi$ using BBP-type formulas”, Ramanujan J., 51 (2020), 177–186 | DOI | MR

[32] B. Edun, “Finite and infinite nested square roots convergent to unity”, Ramanujan J., 51 (2020), 495–500 | DOI | MR

[33] L. Euler, “De miris proprietatibus curvae elasticae sub aequatione $y=\int(xx~dx)/\sqrt{(1-x^4)} $”, Acta Academiae Scientiarum Imperialis Petropolitanae, 1782:II (1786), 34–61