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 …

In 2001 W. Gosper introduced constant Π q, and conjectured many intriguing identities on
this constant. In this paper we employ some knowledge of modular equations with degree 5 …

We give unified modular proofs to all of Gosper's identities on the q-constant Π q. We also
confirm Gosper's observation that for any distinct positive integers n 1,⋯, nm with m≥ 3, Π …

In “Experiments and discoveries in q-trigonometry”, W. Gosper defined the q-analogues sin
q (z) and cos q (z) of sin z and cos z respectively. He also conjectured identities for sin q (2 …

In an interesting article entitled “Experiments and discoveries in q-trigonometry”, RW Gosper
conjectured few beautiful \Pi_q and Lambert series identities. Many people have attempted …

Proof for a Πq-identity of Gosper - ScienceDirect Skip to main contentSkip to article Elsevier
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Applying the theory of modular forms and Lambert series manipulations we establish an
Eisenstein series identity. From this formula we confirm a Lambert series identity conjectured …

The object of this report is q-series and their relationship with certain special functions.
Firstly, Jackson's q-analogue of the Euler gamma function is introduced and a q-analogue …