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Three proofs are given for a reciprocity theorem for a certain q-series found 7 in Ramanujan's lost notebook. The first proof uses Ramanujan's 1 ψ 1 summation the-8 orem, the second employs an identity of N. J. Fine, and the third is combinatorial. 9 Next, we show that the reciprocity theorem leads to a two variable generalization of 10 the quintuple(More)
We show how Rank-Crank type PDEs for higher order Appell functions due to Zwegers may be obtained from a generalized Lambert series identity due to the first author. Special cases are the Rank-Crank PDE due to Atkin and the third author and a PDE for a level 5 Appell function also found by the third author. These two special PDEs are related to generalized(More)