Geodesic
A certain formula of Liouville
Čebyševskij sbornik, Tome 25 (2024) no. 3, pp. 335-342 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: multiple integral, factorial, subfactorial, Euler number.
Mots-clés : Liouville formula, binomial sum 
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     author = {Yu. V. Andrianova and V. B. Sherstyukov},
     title = {A certain formula of {Liouville}},
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Yu. V. Andrianova; V. B. Sherstyukov. A certain formula of Liouville. Čebyševskij sbornik, Tome 25 (2024) no. 3, pp. 335-342. http://geodesic.mathdoc.fr/item/CHEB_2024_25_3_a20/