Approximations and inequalities for the exponential beta function

Abstract

Abstract In this paper, motivated by interest in simulating the expenditure patterns of construction projects, we introduce the mathematical concept of Exponential-Beta function by $$ F ( \alpha ,\beta ) := \int _{0}^{1}\exp \bigl[ x^{\alpha } ( 1-x ) ^{\beta } \bigr]\,dx, $$ F ( α , β ) : = ∫ 0 1 exp [ x α ( 1 − x ) β ] d x , where α, β are positive numbers. Taylor’s-type approximations, several analytic inequalities, and global convexity properties are established.