Monotonicity properties of ratios involving confluent hypergeometric functions of the first kind

In this paper, we establish several new monotonicity properties of the functions \(x ↦ M(a,b;x)/M(c,d;x)\) and \(x ↦ {∑ ᵢ₌₁ᵐ M(aᵢ,bᵢ;x)}{∑ ⱼ₌₁ᵐ M(cⱼ,dⱼ;x)}\) under suitable conditions on the parameters, where \(M(a,b;x)\) denotes the confluent hypergeometric function of the first kind. And then we derive several new inequalities involving the confluent hypergeometric function of the first kind, the incomplete gamma function and the modified Bessel function of the first kind. Furthermore, we generalize some known results.