Ramanujan listed several q-series identities in his lost notebook. The most well-known q-series identities are the Rogers–Ramanujan-type identities. These identities were first discovered by Rogers and then rediscovered by Ramanujan. In this chapter, we prove several infinite families of congruences modulo powers of 2 and multiples of 2 and 3 for the coefficient of an Rogers–Ramanujan-type identity. Some recurrence relations connecting the identity with some partition functions are also defined.

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Results on an Identity of Rogers–Ramanujan Type

  • Sabi Biswas,
  • Nipen Saikia

摘要

Ramanujan listed several q-series identities in his lost notebook. The most well-known q-series identities are the Rogers–Ramanujan-type identities. These identities were first discovered by Rogers and then rediscovered by Ramanujan. In this chapter, we prove several infinite families of congruences modulo powers of 2 and multiples of 2 and 3 for the coefficient of an Rogers–Ramanujan-type identity. Some recurrence relations connecting the identity with some partition functions are also defined.