Sharper bounds and new proofs of the exponential function with cotangent

Xiangyang Wu; Kang Yang; Nichang Jiang; Xiao-Diao Chen; Xiangyang Wu; Kang Yang; Nichang Jiang; Xiao-Diao Chen

doi:10.3934/math.2020450

AIMS Mathematics

2020, Volume 5, Issue 6: 7014-7040. doi: 10.3934/math.2020450

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Research article

Sharper bounds and new proofs of the exponential function with cotangent

Key Laboratory of Complex Systems Modeling and Simulation, Hangzhou Dianzi University, Hangzhou, China

Received: 28 May 2020 Accepted: 06 September 2020 Published: 09 September 2020
MSC : 33B10, 26D05

This paper provides a Páde interpolation based method for finding improved bounds for the exponential function with cotangent. In principle, it can recover many results in prevailing methods. A new method for proving the corresponding bounds is also proposed, which can also be applied for proving more other bounding functions. Numerical experiments show that the new bounds are better than those of prevailing methods.
- bounds,
- inequalities,
- circular functions,
- Páde interpolation,
- cotangent function
Citation: Xiangyang Wu, Kang Yang, Nichang Jiang, Xiao-Diao Chen. Sharper bounds and new proofs of the exponential function with cotangent[J]. AIMS Mathematics, 2020, 5(6): 7014-7040. doi: 10.3934/math.2020450

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Abstract

This paper provides a Páde interpolation based method for finding improved bounds for the exponential function with cotangent. In principle, it can recover many results in prevailing methods. A new method for proving the corresponding bounds is also proposed, which can also be applied for proving more other bounding functions. Numerical experiments show that the new bounds are better than those of prevailing methods.

References

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