Identities of the Rogers-Ramanujan-Slater Type

Andrew V. Sills

doi:10.1142/S1793042107000912

Identities of the Rogers-Ramanujan-Slater Type

Andrew V. Sills

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

It is shown that (two-variable generalizations of) more than half of Slater's list of 130 Rogers–Ramanujan identities (L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math Soc. (2) 54 (1952) 147–167) can be easily derived using just three multiparameter Bailey pairs and their associated q-difference equations. As a bonus, new Rogers–Ramanujan type identities are found along with natural combinatorial interpretations for many of these identities.

Original language	American English
Journal	International Journal of Number Theory
Volume	3
DOIs	https://doi.org/10.1142/S1793042107000912
State	Published - Jun 1 2007

Disciplines

Education
Mathematics

Keywords

Integer Partitions
Rogers-Ramanujan-Slater
q-Difference Equations

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https://doi.org/10.1142/S1793042107000912

Cite this

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AB - It is shown that (two-variable generalizations of) more than half of Slater's list of 130 Rogers–Ramanujan identities (L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math Soc. (2) 54 (1952) 147–167) can be easily derived using just three multiparameter Bailey pairs and their associated q-difference equations. As a bonus, new Rogers–Ramanujan type identities are found along with natural combinatorial interpretations for many of these identities.

KW - Integer Partitions

KW - Rogers-Ramanujan-Slater

KW - q-Difference Equations

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/664

UR - https://doi.org/10.1142/S1793042107000912

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DO - 10.1142/S1793042107000912

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SN - 1793-0421

VL - 3

JO - International Journal of Number Theory

JF - International Journal of Number Theory

ER -

Identities of the Rogers-Ramanujan-Slater Type

Abstract

Disciplines

Keywords

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