Generalizations of Milne’s U ( n + 1 ) q -Chu-Vandermonde summation

Jian-Ping Fang

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 2, page 395-407
  • ISSN: 0011-4642

Abstract

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We derive two identities for multiple basic hyper-geometric series associated with the unitary U ( n + 1 ) group. In order to get the two identities, we first present two known q -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two U ( n + 1 ) q -Chu-Vandermonde summations established by Milne, we arrive at our results. Using the identities obtained in this paper, we give two interesting identities involving binomial coefficients. In addition, we also derive two nontrivial summation equations from the two multiple extensions.

How to cite

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Fang, Jian-Ping. "Generalizations of Milne’s $U(n+1)$$q$-Chu-Vandermonde summation." Czechoslovak Mathematical Journal 66.2 (2016): 395-407. <http://eudml.org/doc/280098>.

@article{Fang2016,
abstract = {We derive two identities for multiple basic hyper-geometric series associated with the unitary $U(n+1)$ group. In order to get the two identities, we first present two known $q$-exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two $U(n+1)$$q$-Chu-Vandermonde summations established by Milne, we arrive at our results. Using the identities obtained in this paper, we give two interesting identities involving binomial coefficients. In addition, we also derive two nontrivial summation equations from the two multiple extensions.},
author = {Fang, Jian-Ping},
journal = {Czechoslovak Mathematical Journal},
keywords = {$U(n+1)$ group; multiple basic hypergeometric series; basic hypergeometric series},
language = {eng},
number = {2},
pages = {395-407},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalizations of Milne’s $U(n+1)$$q$-Chu-Vandermonde summation},
url = {http://eudml.org/doc/280098},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Fang, Jian-Ping
TI - Generalizations of Milne’s $U(n+1)$$q$-Chu-Vandermonde summation
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 395
EP - 407
AB - We derive two identities for multiple basic hyper-geometric series associated with the unitary $U(n+1)$ group. In order to get the two identities, we first present two known $q$-exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two $U(n+1)$$q$-Chu-Vandermonde summations established by Milne, we arrive at our results. Using the identities obtained in this paper, we give two interesting identities involving binomial coefficients. In addition, we also derive two nontrivial summation equations from the two multiple extensions.
LA - eng
KW - $U(n+1)$ group; multiple basic hypergeometric series; basic hypergeometric series
UR - http://eudml.org/doc/280098
ER -

References

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