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.
