Abstract

This entry to the Archive of Formal Proofs defines the Ramanujan theta function and derives from it the more commonly known Jacobi theta function on the unit disc as well as its version in the complex plane and its half-period variants.

The most notable single result in this work is the proof of Jacobi’s triple product and its corollary, Euler’s famous pentagonal number theorem.

BibTeX

@article{Theta_Functions-AFP,
  author  = {Manuel Eberl},
  title   = {Theta Functions},
  journal = {Archive of Formal Proofs},
  month   = {December},
  year    = {2024},
  note    = {\url{https://isa-afp.org/entries/Theta_Functions.html},
             Formal proof development},
  ISSN    = {2150-914x},
}