4 papers
math.CO2026
Non-external Proofs of Lagrange Inversion Formula
Dominik Beck, Piotr MaÄkowiak
The goal of the paper is to present two simple proofs of the Lagrange Inversion Formula for formal power series. Both proofs are non-external in the sense that they use concepts th…
math.CA2025
When Mathematics Helps Physics: Calculation of the Integral of Kholodenko and Silagadze
Dominik Beck
In this paper, we show a physics-free derivation of a Landau-Zener type integral introduced by Kholodenko and Silagadze.
math.MG2025
The Probability that a Random Triangle in a Cube is Obtuse
Dominik Beck
In this paper, we derive the exact formula for the probability that three randomly and uniformly selected points from the interior of the unit cube form vertices of an obtuse trian…
math.MG2024
On Random Simplex Picking Beyond the Blashke Problem
Dominik Beck
New selected values of odd random simplex volumetric moments (moments of the volume of a random simplex picked from a given body) are derived in an exact form in various bodies in…