Gosper-type Lambert series identities of level 14

Abstract

We derive two Gosper-type Lambert series identities of level $14$ which involve the $q$-constant ${\Pi }_q$ using a special case of Bailey's ${}_6{\psi }_6$ summation formula and certain propeties of $\eta$-quotients and generalized $\eta$-quotients on the congruence subgroup ${\Gamma }_0(14)$.

arXiv comment13 pages, revised proofs of Theorems 1.1 and 1.2; comments welcome