Boros-Moll多项式序列递推关系的代数证明

Algebraic proof of recursive relation for Boros-Moll polynomial sequence

为了拓展Boros-Moll多项式序列递推关系的基本理论,研究了Boros-Moll多项式序列递推关系新的证明方法。首先,对Boros-Moll多项式序列满足的递推关系进行适当变形、分拆;其次,将满足的递推关系式构造为3个部分和的差式;最后,运用代数方法、构造法等数学方法得出3个部分的和均为零,进一步得到Boros-Moll多项式序列递推关系的一个新的证明方法。结果表明,在Boros-Moll多项式序列递推关系中,对其结构进行巧妙变形、分拆,再证明相应的引理成立,可得出一个新的证明方法。研究结果丰富了Boros-Moll多项式序列递推关系的相关理论,为Boros-Moll多项式序列在组合数学、社会科学、信息论等领域的应用提供了理论参考。

In order to expand the basic theory of the recurrence relationship of Boros-Moll polynomial sequence,a new proof method for the recurrence relationship of Boros-Moll polynomial sequence was studied.Firstly,the recurrence relationship satisfied by the Boros-Moll polynomial sequence was appropriately deformed and partitioned.Secondly,the recursive relationship that satisfies as the difference of the sum of three parts was constructed.Finally,mathematical methods such as algebraic method and structured approach were used to find that the sum of the three parts is all zero.Furthermore,a new proof method for the recurrence relationship of Boros-Moll polynomial sequence was obtained.The results indicate that in the Boros-Moll polynomial sequence recurrence relationship,the recurrence relationship is cleverly deformed and partitioned,and the corresponding lemma is proved to be corrected,thus obtaining a new proof method.The research results enrich the relevant theory of recurrence relationship of the Boros-Moll polynomial sequence,and provide a certain theoretical reference value for the application of the Boros-Moll polynomial sequence in combinatorics,social science,information theory and other fields.