Approximations and inequalities for the exponential beta function

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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):=∫01exp[xα(1−x)β]dx, whereα,βare positive numbers. Taylor’s-type approximations, several analytic inequalities, and global convexity properties are established.

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