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The Rogers-Ramanujan Identities

Author

Listed:
  • Hossain, Fazlee
  • Das, Sabuj

Abstract

In 1894, Rogers found the two identities for the first time. In 1913, Ramanujan found the two identities later and then the two identities are known as The Rogers-Ramanujan Identities. In 1982, Baxter used the two identities in solving the Hard Hexagon Model in Statistical Mechanics. In 1829 Jacobi proved his triple product identity; it is used in proving The Rogers-Ramanujan Identities. In 1921, Ramanujan used Jacobi’s triple product identity in proving his famous partition congruences. This paper shows how to generate the generating function for , , and , and shows how to prove the Corollaries 1 and 2 with the help of Jacobi’s triple product identity. This paper shows how to prove the Remark 3 with the help of various auxiliary functions and shows how to prove The Rogers-Ramanujan Identities with help of Ramanujan’s device of the introduction of a second parameter a.

Suggested Citation

  • Hossain, Fazlee & Das, Sabuj, 2015. "The Rogers-Ramanujan Identities," MPRA Paper 83043, University Library of Munich, Germany, revised 28 Mar 2015.
    • Handle: RePEc:pra:mprapa:83043
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    File URL: https://mpra.ub.uni-muenchen.de/83043/1/MPRA_paper_83043.pdf
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    References listed on IDEAS

    as
    1. Das, Sabuj & Mohajan, Haradhan, 2014. "Generating Functions for and," MPRA Paper 55684, University Library of Munich, Germany, revised 22 Jan 2014.
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    Cited by:

    1. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Aspects of Profit Maximization if Cost of Principal Raw Material Increases," MPRA Paper 117453, University Library of Munich, Germany, revised 22 Mar 2023.
    2. Mohajan, Devajit, 2023. "Mathematical Analysis of an Industry When Cost of Principal Raw Materials Increase: A Nonlinear Budget Constraint Attempt," MPRA Paper 118933, University Library of Munich, Germany.

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    More about this item

    Keywords

    At most; auxiliary function; convenient; expansion; minimal difference; operator; Ramanujan’s device.;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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