Properties of Gauss Hypergeometric function, 2F1, of special parameters

This paper studies some properties of Gauss Hypergeometric function, \({}_2F_1(a, b, c; -t^{2n})\),of specific parameters \(a= 1/2n, b \geq 0, c = 1/2n +1, n \in \mathbb{N}^+ \) . Generating equation is presented and basic properties, monotonicity, bounded range, and inequality are discussed. With these parameters, \({}_2F_1\) is monotonic decreasing function for \(|t|\) value, bounded on range and \({}_2F_1(, b_1,) > {}_2F_1(, b_2,), \forall 0 \leq b_1 < b_2, b_1, b_2 \in \mathbb{R}\)