342 research outputs found
Human proofs of identities by Osburn and Schneider
Osburn and Schneider derived several combinatorial identities involving
harmonic numbers using the computer programm Sigma. Here, they are derived by
partial fraction decomposition and creative telescoping
A continued fraction expansion for a q-tangent function: An elementary proof
We prove a continued fraction expansion for a certain -tangent function
that was conjectured by the present writer, then proved by Fulmek, now in a
completely elementary way
On Touchard's continued fraction and extensions: combinatorics-free, self-contained proofs
We give a direct and simple proof of Touchard's continued fraction, provide
an extension of it, and transform it into similar expansions related to Motzkin
and Schroeder numbers. Another proof is then given that uses only induction. We
use this machinery on two examples that appear in recent papers of
Josuat-Verges; with an additional parameter, these two can be treated
simultaneously
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