Algebraic proof of recursive relation for Boros-Moll polynomial sequence

Abstract

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.

Keywords

• combinatorics; boros-moll polynomial sequence; recursive relation; algebraic proof; structured approach