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Continued fraction expansions for q-tangent and q-cotangent functions

Abstract : For 3 different versions of q-tangent resp. q-cotangent functions, we compute the continued fraction expansion explicitly, by guessing the relative quantities and proving the recursive relation afterwards. It is likely that these are the only instances with a ''nice'' expansion. Additional formulae of a similar type are also provided.
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Helmut Prodinger. Continued fraction expansions for q-tangent and q-cotangent functions. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (2), pp.47-64. ⟨hal-00990445⟩

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