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The authors establish the necessary and sufficient conditions under whichcertain combinations of Gaussian hypergeometric function and elementaryfunction are monotone in the parameter, which generalize the recent results ofgeneralized elliptic integrals of the first and second kinds obtained by Qiu etal. Moreover, the authors also prove two monotonicity theorems of generalizedelliptic integrals from another point of view.

Monotonicity Properties of Gaussian Hypergeometric Functions with Respect to the Parameter