Generalization of five q-series identities of Ramanujan and unexplored weighted partition identities

Bhoria, Subhash Chand; Eyyunni, Pramod; Maji, Bibekananda

doi:10.1007/s11139-021-00529-1

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…(Bressoud and Subbarao's proof was combinatorial). Moreover, the authors of [11] even generalized the result of Bressoud and Subbarao.…”

Section: Introductionmentioning

confidence: 76%

“…The proof of this identity given in [11] begins with (2.7) and is quite long (see p. 446-449 of [11]).…”

Section: (Finite Analogue Of Entry 1)mentioning

confidence: 99%

“…This theorem also has many beautiful consequences in q-series and partition theory. First of all, from this single identity, the authors of [11] could derive all five entries in the unorganized portion of Ramanujan's second and third notebooks [17, pp. 354-355] (see also [19, pp.…”

Section: Introductionmentioning

confidence: 99%

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A finite analogue of a $q$-series identity of Bhoria, Eyyunni and Maji and its applications

Dixit¹,

Patel²

2022

Preprint

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Bhoria, Eyyunni and Maji recently obtained a four-parameter q-series identity which gives as special cases not only all five entries of Ramanujan on pages 354 and 355 of his second notebook but also allows them to obtain an analytical proof of a result of Bressoud and Subbarao. Here, we obtain a finite analogue of their identity which naturally gives finite analogues of Ramanujan's results. Using one of these finite analogues, we deduce an identity for a finite sum involving a 2 φ 1 . This identity is then applied to obtain a generalization of the generating function version of Andrews' famous identity for the smallest parts function spt(n). The q-series which generalizes ∑ ∞ n=1 spt(n)q n is completely different from S(z, q) considered by Andrews, Garvan and Liang. Further applications of our identity are given. Lastly we generalize a result of Andrews, Chan and Kim which involves the first odd moments of rank and crank.

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“…(Bressoud and Subbarao's proof was combinatorial). Moreover, the authors of [11] even generalized the result of Bressoud and Subbarao.…”

Section: Introductionmentioning

confidence: 76%

“…The proof of this identity given in [11] begins with (2.7) and is quite long (see p. 446-449 of [11]).…”

Section: (Finite Analogue Of Entry 1)mentioning

confidence: 99%

See 1 more Smart Citation

A finite analogue of a $q$-series identity of Bhoria, Eyyunni and Maji and its applications

Dixit¹,

Patel²

2022

Preprint

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Bressoud–Subbarao Type Weighted Partition Identities for a Generalized Divisor Function

et al. 2023

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A finite analogue of a q-series identity of Bhoria, Eyyunni and Maji and its applications

Dixit

Patel

2023

Discrete Mathematics

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Generalization of five q-series identities of Ramanujan and unexplored weighted partition identities

Cited by 3 publications

References 19 publications

A finite analogue of a $q$-series identity of Bhoria, Eyyunni and Maji and its applications

A finite analogue of a $q$-series identity of Bhoria, Eyyunni and Maji and its applications

Bressoud–Subbarao Type Weighted Partition Identities for a Generalized Divisor Function

A finite analogue of a q-series identity of Bhoria, Eyyunni and Maji and its applications

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