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Inequalities and bounds for generalized complete elliptic integrals |
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| Authors: | Edward Neuman |
| Affiliation: | Department of Mathematics, Mailcode 4408, Southern Illinois University, 1245 Lincoln Drive, Carbondale, IL 62901, USA |
| Abstract: | Computable bounds for the generalized complete elliptic integrals of the first and second kind are obtained. Also, bounds for some combinations and products for integrals under discussion are established. It has been proven that both families of integrals are logarithmically convex as functions of the first parameter. This property has been employed to obtain several inequalities involving integrals in question. |
| Keywords: | Generalized complete elliptic integrals of the first and second kind Gauss' hypergeometric function Power mean Logarithmic convexity Concavity/convexity Inequalities Lower and upper bounds |
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