Geodesic
On integration of functions of complexity one
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 496-502.

Voir la notice de l'article provenant de la source Math-Net.Ru

We describe functions of complexity one with antiderivative of the same complexity.
Keywords: falsity of analytic functions, complexity classes, integration. 
@article{JSFU_2019_12_4_a11,
     author = {Valery K. Beloshapka},
     title = {On integration of functions of complexity one},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {496--502},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a11/}
}
TY  - JOUR
AU  - Valery K. Beloshapka
TI  - On integration of functions of complexity one
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2019
SP  - 496
EP  - 502
VL  - 12
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a11/
LA  - en
ID  - JSFU_2019_12_4_a11
ER  - 
%0 Journal Article
%A Valery K. Beloshapka
%T On integration of functions of complexity one
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2019
%P 496-502
%V 12
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a11/
%G en
%F JSFU_2019_12_4_a11
Valery K. Beloshapka. On integration of functions of complexity one. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 496-502. http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a11/

[1] J. Liouville, “Sur la détermination des intégrales dont la valeur est algébrique”, Journal de l'ecole polytechnique, XIV, Sec. 23 (1833) | MR

[2] J.F. Ritt, Integration in finite term, Liouville's theory of elementary methods, Colombia University Press, NY, 1948 | MR

[3] V.K. Beloshapka, “Analytic Complexity of Functions of Two Variables”, Russ. J. Math. Phys., 14:3 (2007), 243–249 | DOI | MR | Zbl

[4] V.K. Beloshapka, “Algebraic Functions of Complexity One, a Weierstrass Theorem, and Three Arithmetic Operations”, Russian Journal of Mathematical Physics, 23:3 (2016), 343–347 | DOI | MR | Zbl

[5] V.K. Beloshapka, “Decomposition of Functions of Finite Analytical Complexity”, Journal of Siberian Federal University. Mathematics Physics, 11:6 (2018), 680–685 | DOI | MR