A new asymptotic expansion is derived for the incomplete beta function I(a, b, x), which is suitable for large a, small b and $x > 0.5$. This expansion is of the form ...

In this paper, we consider the function f p ( t )= 2p X 2 ( 2p t+p;p ) , where χ²(x; n) defined by X 2 ( x;p )= 2 −p/2 Γ( p/2 ) e −x/2 x p/2−1 , is the density function of a χ²-distribution with n ...

Function spaces and asymptotic analysis are essential areas of mathematical research that explore the properties and behaviors of functions under various conditions. Function spaces, such as Besov and ...

Most mathematical models do not admit exact solutions. Asymptotic and perturbation methods provide powerful techniques for obtaining approximate solutions, which allow one to draw physical conclusions ...

Function spaces form a fundamental framework in modern mathematical analysis, allowing researchers to systematically study functions through norms, metrics and topological properties. Asymptotic ...