Geodesic
Continued fractions related to \((t,q)\)-tangents and variants
The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2
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For the $q$-tangent function introduced by Foata and Han (this volume) we provide the continued fraction expansion, by creative guessing and a routine verification. Then an even more recent $q$-tangent function due to Cieslinski is also expanded. Lastly, a general version is considered that contains both versions as special cases.
DOI : 10.37236/2014
Classification : 05A30, 05A10, 11A55
Mots-clés : \(q\)-trigonometric functions, \(q\)-tangent function, continued fraction expansion 
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     author = {Helmut Prodinger},
     title = {Continued fractions related to \((t,q)\)-tangents and variants},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {2},
     doi = {10.37236/2014},
     zbl = {1230.05050},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2014/}
}
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Helmut Prodinger. Continued fractions related to \((t,q)\)-tangents and variants. The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2. doi: 10.37236/2014

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