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- W4297126827 abstract "For a ? (0,1/2] and r ? (0,1), let Ka(r) (K (r)) denote the generalized elliptic integral (complete elliptic integral, respectively) of the first kind. In this article, we mainly present a sufficient and necessary condition under which the function a ? [K(r)-Ka(r)]=(1-2a)?(?? R) is monotone on (0,1/2) for each fixed r ? (0,1). The obtained result leads to the conclusion that inequality K (r)- (1-2a)? [K(r)- ?/2] ? Ka(r) ? K (r)-(1-2a)? [K(r)-?/2] holds for all a ? (0,1/2] and r ? (0,1) with the best possible constants ? = ?/2 and ? = 2." @default.
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- W4297126827 date "2022-01-01" @default.
- W4297126827 modified "2023-10-14" @default.
- W4297126827 title "A monotonicity theorem for the generalized elliptic integral of the first kind" @default.
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- W4297126827 doi "https://doi.org/10.2298/aadm201005031b" @default.
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