Chapter 16 of Ramanujan’s second notebook: theta-functions and 𝑞-series

Partition bijections, a survey

“…1 The way we see it, finding direct bijective or involutive proofs or most identities is an infeasible task. Right now very few partition identities have such proofs and it seems there is little reason why the remaining identities should be so fortunate to have them, especially after resisting a combinatorial proof for so many years.…”

New Properties for The Ramanujan’S Continued Fraction of Order 12

“…The Jacobi triple product identity [1] in Ramanujan's notation is ( , ) = ( ; ) ( ; ) ( ; ) . f a b a ab b ab ab ab…”

“…Jacobi's triple product identity is a special case of 1 1 ψ summation formula [1] due to Ramanujan. S. Bhargava et al [6] made use of Ramanujan's 1 1 ψ summation formula to prove a convolution identity for certain coefficientsgenerated by the quotient of two infinite products.…”

Back Matter

“…Math. Monthly 86,no. 2,[89][90][91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106][107][108] [ [166] Komatsu, T. (2003), On Tasoev's continued fractions.…”

“…134,no. 1,[1][2][3][4][5][6][7][8][9][10][11][12]88,193,212,272,288,289 bilateral Bailey pairs,139,148,173,174,183 bilateral Bailey transform asymmetric,169,[171][172][173]169,[171][172][173] 83,95,162,164,165,[167][168][169][170]172,175,184 Andrews and Warnaar,172,173 Rowell,[168][169][170]184 Schilling and Warnaar,162,…”