• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.2
• /
• pp.97-107
• /
• 2007

Ramanujan gave six identities involving ${\theta}$-function expansion. We extended these identities by introducing a free parameter. We also give the interpretation of one of the identities using theory of partitions.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.937-956
• /
• 2018

This article gives the foundations of the colored Jones polynomial for singular knots. We extend Masbum and Vogel's algorithm [26] to compute the colored Jones polynomial for any singular knot. We also introduce the tail of the colored Jones polynomial of singular knots and use its stability properties to prove a false theta function identity that goes back to Ramanujan.