Generalized Lambert series identities

Abstract

We present two infinite families of generalized Lambert series identities, and deduce several known identities from them. They include an identity due to M. Jackson, a corollary of Ramanujan's 1ψ1‐summation formula, and a recent identity of G. E. Andrews, R. P. Lewis and Z.‐G. Liu. 2000 Mathematics Subject Classification 33D15, 11D85.

Automorphic Properties of Generating Functions for Generalized Rank Moments and Durfee Symbols

“…Taking (a 1 , a 2 , b 1 , b 2 , b 3 , q) = (−x, −xq, xζ, x/ζ, x, q 2 ) in the case (r, s) = (2, 3) of Theorem 2.1 of [16], we obtain…”

On recursions for coefficients of mock theta functions

“…Replacing q, a, b and c by q 6 , q 5 , q 5 and −1/q 2 , respectively, in ( [8], Corollary 3.2), we obtain…”

“…Similarly, we replace a = 2k + 1 and b = 6l + 5 in the second sum. This leads us to 8) where in the last equality, we replaced l by −l − 1 in the second sum. Similarly, the generating function for…”

“…In [8], the first author proved the following generalized Lambert series identity: where the ith term of the sum is obtained from the first by interchanging a 1 and a i . Identity (1.1) is of interest for several reasons.…”

Back Matter

“…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. Math.…”