An Integral of a Polynomial with Multiple Roots

A. E. Guterman, S. V. Danielyan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A full integral of a polynomial is defined as its integral with the property that any multiple root of the polynomial is a root of this integral. The paper investigates relationships between the existence of a full integral and the form of a polynomial. In particular, it is proved that a full integral exists if the polynomial has no more than one multiple root. On the other hand, if the number of multiple roots of a polynomial strictly exceeds the number of its simple roots increased by one, then the polynomial has no full integral. Bibliography: 7 titles.

Original languageEnglish
Pages (from-to)128-138
Number of pages11
JournalJournal of Mathematical Sciences
Issue number2
StatePublished - 1 Aug 2020
Externally publishedYes

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