Cubic and quintic analogues of Ramanujan's septic theta function identity

2023/12/24 by Bruce C. Berndt, Berndt, Bruce C., Örs Rebák +1 · 2 citations
Mathematics · Physics and Astronomy · #05A30 #11F27 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Historical Astronomy and Related Studies #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2312.15513

openalex publication_date 2023/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On page 206 in his lost notebook, Ramanujan recorded an incomplete septic theta function identity. Motivated by the completion of this identity by the second author, we offer cubic and quintic analogues. Using the theory generated by these two analogues and Ramanujan's class invariants, we provide many evaluations for Ramanujan's most prominent theta function, φ(q) in his notation.

Cited by

• The Rogers--Ramanujan continued fraction
• Ninth degree analogue of Ramanujan's septic theta function identity

Related

• Ninth degree analogue of Ramanujan's septic theta function identity
• On Ramanujan's cubic continued fraction and explicit evaluations of theta-functions
• A Unified Transformation Formula for Ramanujan's Theta Function
• Several q-series related to Ramanujan's theta functions
• New Proofs of Ramanujan's Identities on False Theta Functions