Truncated sums for the partition function and a problem of Merca

In 2012, Andrews and Merca established a truncated form of Euler’s pentagonal number theory. In this note, using the Rogers–Fine identity, we present a partition theoretic interpretation of truncated sums on the partition function which solve a problem given by Merca. Furthermore, we prove an inequa...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2022, Vol.116 (1), Article 22
Main Authors: Xia, Ernest X. W., Zhao, Xiang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Number theory
Original Paper
Partitions (mathematics)
Sums
Theoretical
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Summary:In 2012, Andrews and Merca established a truncated form of Euler’s pentagonal number theory. In this note, using the Rogers–Fine identity, we present a partition theoretic interpretation of truncated sums on the partition function which solve a problem given by Merca. Furthermore, we prove an inequality on ordinary partition which implies the positive result on truncated sums of partition function due to Andrews and Merca.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-021-01167-4