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  5. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.48 (2016)
  6. Notes on a combinatorial identity
 
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Notes on a combinatorial identity

Alzer, Horst
•
Prodinger, Helmut
2016
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ISSN
0049-4704
DOI
10.13137/2464-8728/13171
http://hdl.handle.net/10077/13171
  • Article

e-ISSN
2464-8728
Abstract
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.
Series
Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics
48 (2016)
Subjects
  • Combinatorial identit...

  • q-binomial coefficien...

  • completely monotonic

  • partial fraction deco...

Publisher
EUT Edizioni Università di Trieste
Licence
http://creativecommons.org/licenses/by-nc-nd/4.0/
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