2025/02/14 by Giraldi, Filippo
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2502.10483
The Fox H-function is a special function which is defined via the Mellin-Barnes integrals and produces, as particular cases, Wright generalized hypergeometric functions, MacRobert's E-functions and Meijer G-functions, to name but few. Various cases of non-negative Fox H-functions are obtained in literature by relying on the properties of integral transforms and the complete monotonicity. In the present scenario, Fox H-functions, which are positive on ℝ+, are determined via the Mellin convolution products of finite combinations, with possible repetitions, of elementary functions. The chosen elementary functions are non-negative on ℝ+ and are defined via stretched exponential and power laws. Further forms of positive Fox H-functions can be obtained from the former via elementary properties and integral transforms. As particular cases, we determine forms of Wright generalized hypergeometric functions, MacRobert's E-functions and Meijer G-functions which are positive on ℝ+.