June 2022 Asymptotically sharp bounds for the complete $p$-elliptic integral of the first kind
Ti-Ren HUANG, Lu CHEN, Yu-Ming CHU
Author Affiliations +
Hokkaido Math. J. 51(2): 189-210 (June 2022). DOI: 10.14492/hokmj/2019-212

Abstract

In the article, we present several monotonicity and convexity properties involving the complete $p$-elliptic integral $\mathcal{K}_{p}(r)$ of the first kind, and provide several asymptotically sharp bounds for $\mathcal{K}_{p}(r)$.

Funding Statement

This research was supported by the Natural Science Foundation of China (Grant Nos. 11701176, 61673169, 11301127, 11626101, 11601485).

Citation

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Ti-Ren HUANG. Lu CHEN. Yu-Ming CHU. "Asymptotically sharp bounds for the complete $p$-elliptic integral of the first kind." Hokkaido Math. J. 51 (2) 189 - 210, June 2022. https://doi.org/10.14492/hokmj/2019-212

Information

Received: 13 December 2019; Published: June 2022
First available in Project Euclid: 9 September 2022

Digital Object Identifier: 10.14492/hokmj/2019-212

Subjects:
Primary: 26A48 , 26D07. , 33C05 , 33E05

Keywords: complete $p$-elliptic integral , complete elliptic integral , convexity , Monotonicity

Rights: Copyright c 2022 Hokkaido University, Department of Mathematics

Vol.51 • No. 2 • June 2022
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