A certain formula of Liouville
https://doi.org/10.22405/2226-8383-2024-25-3-335-342
Abstract
The classical Liouville formula expressing the multiple integral over a multidimensional
pyramid through the integral over a segment is discussed. It is shown how the Liouville formula
is related to the special sum, containing successive antiderivatives of the integrand. Specific examples are given to illustrate the general result. Along the way, a compact formula for calculating the power moments of an exponential function is proved.
About the Authors
Yulia Vladimirovna Andrianova
Lomonosov Moscow State University
Russian Federation
Russian Federation
Vladimir Borisovich Sherstyukov
Lomonosov Moscow State University; Moscow Center of Fundamental and Applied Mathematics
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
References
1. Vinogradova, I. A., Olekhnik, S.N., Sadovnichii, V. A. 2018, “Mathematical analysis in tasks
2. and exercises”, MCСME, Moscow, 256 pp.
3. Fikhtengol’ts, G. M. 1966, “A Course of Differential and Integral Calculus”, Nauka, Moscow,
4. Vol. 3, 656 pp.
5. Gel’fond, A. O. 2006, “Residues and Their Applications”, KomKniga, Moscow, 112 pp.
6. Prudnikov, A.P., Brychkov, Yu. A., Marichev, O. I. 1981, “Integrals and Series. Elementary
7. functions”, Nauka, Moscow, 800 pp.
8. Graham, R. L., Knuth, D. E., Patashnik, O. 1994, “Concrete mathematics: A Foundation for
9. Computer Science”, 2nd edition. Addison-Wesley, MA, xiv+657 pp.
10. Hassani, M. 2003, “Derangements and applications”, Journal of Integer Sequences, vol. 6. Article 03.1.2.
Review
For citations:
Andrianova Yu.V., Sherstyukov V.B. A certain formula of Liouville. Chebyshevskii Sbornik. 2024;25(3):335-342. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-3-335-342
Views:
89
Email this article 