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Title: Notes on a combinatorial identity
Authors: Alzer, Horst
Prodinger, Helmut
Keywords: Combinatorial identityq-binomial coefficientcompletely monotonicpartial fraction decomposition
Issue Date: 2016
Publisher: EUT Edizioni Università di Trieste
Series/Report no.: Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics
48 (2016)
We present a short and simple proof by induction for
where ٢، > 1 is an integer and m 1— ,() ب,..., —n is ٠. complex number.
This is ٠. q-analogue ٠/ a combinatorial identity obtained by Kirschen-
hofer (1996) and Larcombe, Fennessey, and Koepf (2004). Moreover,
we show that the alternating q-binomial .أس?؟ is completely monotonic
with respect ،٠ m, if m > 0 and رل,ه) ع و• The general case where
the exponent ‘ث is replaced by ٠. positive integer d is dealt with using the
elementary technique of partial fraction decomposition.
Type: Article
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/13171
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.48 (2016)

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