Truncated sums for certain restricted partition functions and transformation formulas for basic hypergeometric series

In 2012, a truncated version for the Euler pentagonal number theorem was established by Andrews and Merca. Since then, a series of papers on the subject have followed. In this paper, using some transformation formulas for basic hypergeometric series, we prove several truncated sums for four restrict...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 117; no. 3
Main Author: Yao, Olivia X. M.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.07.2023
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
Primary 11P81
Partitions
Theta series
Truncated series
Basic hypergeometric series
Transformation formulas
05A17
ISSN:1578-7303, 1579-1505
Online Access:Get full text
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Summary:In 2012, a truncated version for the Euler pentagonal number theorem was established by Andrews and Merca. Since then, a series of papers on the subject have followed. In this paper, using some transformation formulas for basic hypergeometric series, we prove several truncated sums for four restricted partitions: partitions with even parts distinct, partitions into distinct non-multiples of four, (2, 3)-regular partitions and overpartitions into odd parts. In particular, we establish new identities and inequalities for these restricted partition functions.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-023-01436-4