Is it a variant of Vandermonde convolution formula for falling factorials? What is the answer? See the picture.
For detailed information on the above results, please read the preprint
F. Qi, D. Lim, and Y.-H. Yao, Notes on two kinds of special values for the Bell polynomials of the second kind, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01757740
which will be activated in a few days.
There are also a few variants of these types of identities for the generalized factorial functions I define in my article: https://cs.uwaterloo.ca/journals/JIS/VOL20/Schmidt/schmidt14.html. See Section 5 and Section 6.
Dear Professor, Feng Qi,
I would like to inform you that several generalizations and variations of Vandermonde convolution formula (sometimes called Chu-Vandermonde identity) are presented in my recent paper available at https://www.researchgate.net/publication/326681752_Several_generalizations_and_variations_of_Chu-Vandermonde_identity (preprint at arXiv, July 2018). I believe that some of identities of this paper can be extended in terms of falling or/and raising factorials.
Best regards,
Romeo
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