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推广的Wallis数列的单调性
Monotonicity of Generalized Wallis Sequences

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Date
2017
Author
严志丹
王伟
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  • 数学科学-已发表论文 [2662]
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Abstract
讨论了推广的Wallis数列n+c∫π20sinnxdx(n≥1,c为非负常数)的单调性.黄永忠等(2016)证明了当0≤c≤12该数列严格递增;当12
 
Let yn(c)=n+c∫π20sinn(x)dx(n=1,2,…;c≥0).Huang et.al(2016)proved that the sequence{yn(c)}is strictly increasing if0≤c≤12,and it is strictly decreasing for sufficiently large n if12<c≤1.We give a new proof of this result and give some discussions on related problems.Moreover,we show that the sequence{yn(c)}is strictly decreasing if and only if c>2π2-1616-π2=0.609945….
 
Citation
大学数学,2017,(6)
URI
https://dspace.xmu.edu.cn/handle/2288/165268

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