Gosper's Lambert series identities of level $14$

TL;DR

This paper derives two new Lambert series identities at level 14 involving the q-constant Pi_q, utilizing Bailey's summation and properties of eta-quotients on the subgroup Gamma_0(14).

Contribution

It introduces novel Lambert series identities at level 14, expanding the understanding of q-series and eta-quotients related to modular forms.

Findings

Derived two Lambert series identities of level 14 involving Pi_q.

Utilized Bailey's $_6 ext{-} ext{psi}_6$ summation formula.

Analyzed properties of eta-quotients on Gamma_0(14).

Abstract

We derive two Gosper's 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 $\Gamma_0(14)$.