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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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
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Abstract	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.
AbstractList	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.
ArticleNumber	106
Author	Yao, Olivia X. M.
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References	Hirschhorn, Sellers (CR14) 2006; 10 Yee (CR30) 2015; 130 Chen (CR8) 2014; 325 Gasper, Rahman (CR11) 2004 Merca (CR19) 2016; 32 Zhang (CR31) 2022; 42 Guo, Zeng (CR13) 2013; 120 CR15 CR12 Andrews (CR2) 1966; 33 CR10 Yao (CR28) 2022; 345 Andrews, Hirschhorn, Sellers (CR4) 2010; 23 Mao (CR17) 2015; 130 Chern (CR9) 2019; 189 Xia, Yee, Zhao (CR26) 2022; 101 McLaughlin, Parsell (CR18) 2012; 28 CR3 Chan, Ho, Mao (CR7) 2016; 169 CR6 CR5 CR27 Yao (CR29) 2022; 65 Merca, Wang, Yee (CR22) 2019; 23 Merca (CR21) 2022; 31 Lebesgue (CR16) 1840; 5 Wang, Yee (CR24) 2019; 166 Xia (CR25) 2022; 137 Merca (CR20) 2021; 30 Rogers (CR23) 1917; 16 Andrews (CR1) 1966; 17 G Gasper (1436_CR11) 2004 M Merca (1436_CR22) 2019; 23 EXW Xia (1436_CR26) 2022; 101 C Wang (1436_CR24) 2019; 166 SH Chan (1436_CR7) 2016; 169 GE Andrews (1436_CR1) 1966; 17 MD Hirschhorn (1436_CR14) 2006; 10 S Chern (1436_CR9) 2019; 189 1436_CR10 J McLaughlin (1436_CR18) 2012; 28 1436_CR15 M Merca (1436_CR20) 2021; 30 M Merca (1436_CR21) 2022; 31 OXM Yao (1436_CR29) 2022; 65 EXW Xia (1436_CR25) 2022; 137 1436_CR12 GE Andrews (1436_CR4) 2010; 23 M Merca (1436_CR19) 2016; 32 AJ Yee (1436_CR30) 2015; 130 1436_CR3 1436_CR5 VA Lebesgue (1436_CR16) 1840; 5 WJ Zhang (1436_CR31) 2022; 42 SC Chen (1436_CR8) 2014; 325 1436_CR6 GE Andrews (1436_CR2) 1966; 33 OXM Yao (1436_CR28) 2022; 345 R Mao (1436_CR17) 2015; 130 LJ Rogers (1436_CR23) 1917; 16 VJW Guo (1436_CR13) 2013; 120 1436_CR27
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Title	Truncated sums for certain restricted partition functions and transformation formulas for basic hypergeometric series
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