Lambert series and Liouville's identities
A. Alaca ; Ş. Alaca ; E. McAfee ; K. S. Williams
GDML_Books, (2007), p.

The relationship between Liouville’s arithmetic identities and products of Lambert series is investigated. For example it is shown that Liouville’s arithmetic formula for the sum ∑(a,b,x,y)∈ℕ⁴ax+by=n(F(a-b)-F(a+b)), where n ∈ ℕ and F: ℤ → ℂ is an even function, is equivalent to the Lambert series for (∑n=1∞(qⁿ/(1-qⁿ))sinnθ)² (θ ∈ ℝ, |q| < 1) given by Ramanujan.

EUDML-ID : urn:eudml:doc:285958 
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm445-0-1,
     author = {A. Alaca and \c S. Alaca and E. McAfee and K. S. Williams},
     title = {Lambert series and Liouville's identities},
     series = {GDML\_Books},
     year = {2007},
     zbl = {1113.11004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm445-0-1}
}

A. Alaca; Ş. Alaca; E. McAfee; K. S. Williams. Lambert series and Liouville's identities. GDML_Books (2007),  http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm445-0-1/