arXiv subjects

Trinh Duc Tai

Publications and source records attributed to Trinh Duc Tai.

2 recordsLinked to original sources

arXiv2018

Volume of sublevel sets versus area of level sets via Gelfand-Leray form

In this paper we give a relation between the volume of sublevel sets and the area of level sets using a Gelfand-Leray form. As a consequence, we give an estimation of the volume of sublevel sets. In particular we give a proof of the known fact that the derivative of the volume of a $n$-dimensional ball with respect to the radius equals the area of the sphere which bounds the $n$-dimensional ball.

math.CA↗

arXiv2011

The generalized gamma functions

In this paper, we introduce a way to generalize the Euler's gamma function as well as some related special functions. With a given polynomial in one variable $f(t)\ge 0$, we can associate a function, so-called "gamma function associated with $f$", defined by $Γ_f(s) := \int_0^\infty f^{s-1} e^{-t} dt$. This function has many features similar to the Euler's gamma function. We also present some initial results on the gamma-type functional equation for $Γ_f(s)$ in some special cases.

math.CV↗