Basis partition polynomials, overpartitions and the Rogers–Ramanujan identities

• George E. Andrews ^[1]
  1. [1] Pennsylvania State University

     Pennsylvania State University

     Borough of State College, Estados Unidos

     
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 197, Nº 1 (September 2015), 2015 (Ejemplar dedicado a: Special Issue Dedicated to Dick Askey on the occasion of his 80th birthday), págs. 62-68
• Idioma: inglés
• DOI: 10.1016/j.jat.2014.05.008
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• Resumen

  • In this paper, a common generalization of the Rogers–Ramanujan series and the generating function for basis partitions is studied. This leads naturally to a sequence of polynomials, called BsP-polynomials. In turn, the BsP-polynomials provide simultaneously a proof of the Rogers–Ramanujan identities and a new, more rapidly converging series expansion for the basis partition generating function. Finally the basis partitions are identified with a natural set of overpartitions.