New fifth and seventh order mock theta function identities

Frank Garvan

New fifth and seventh order mock theta function identities

Number Theory 2019-07-11 v1 Combinatorics

Authors: Frank Garvan

Abstract

We give simple proofs of Hecke-Rogers indefinite binary theta series identities for the two Ramanujan fifth order mock theta functions $\chi_0(q)$ and $\chi_1(q)$ and all three of Ramanujan's seventh order mock theta functions. We find that the coefficients of the three mock theta functions of order 7 are surprisingly related.

Keywords

ramanujan identities and series

Cite

@article{arxiv.1907.04803,
  title  = {New fifth and seventh order mock theta function identities},
  author = {Frank Garvan},
  journal= {arXiv preprint arXiv:1907.04803},
  year   = {2019}
}

Comments

16 pages, accepted to appear in the GEA80 Special Issue of the Annals of Combinatorics

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