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A short proof of the q-Dixon identity

Victor J.W. Guo, Jiang Zeng
2005 Discrete Mathematics  
We give a simple proof of Jackson's terminating q-analogue of Dixon's identity.  ...  Hence, our polynomial argument is somehow equivalent to the role played by the q-Pfaff-Saalschütz identity in the proof of the q-Dixon identity.  ...  In the last twenty years several short proofs of Dixon's identity have been published [3] [4] [5] .  ... 
doi:10.1016/j.disc.2005.04.006 fatcat:lbj5dx63fnd3vgjbuk62z5rfry

Contents

2005 Discrete Mathematics  
Reidys On certain morphisms of sequential dynamical systems 245 Notes V.J.W. Guo and J. Zeng A short proof of the q-Dixon identity 259 B. Wu, L. Zhang and Z.  ...  Stacho Edge-disjoint spanners in Cartesian products of graphs 167 Y. Hong and X.-D. Zhang Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees 187 A.  ... 
doi:10.1016/s0012-365x(05)00314-6 fatcat:6suufuqjorgfxnwx4djkqep5pu

Character Sum Identities in Analogy with Special Functions Identities

Anna P. Helversen-Pasotto
1997 Advances in Mathematics  
For a short direct proof of the finite Barnes identity see [HP 91] , for a simultaneous proof of the classical and the finite identity see [HS] , for a connection with the principal series representations  ...  For a proof of the identity via the representations and characters of GL(3, F q ) (see [HP 82] , where you can find also some more complicated identities).  ... 
doi:10.1006/aima.1997.1637 fatcat:jlcmkpcnyjcblhprwkqo36ca34

Index

2004 Journal of symbolic computation  
and computer analysis, 463 Publisher's Note, 1 qMultiSum-a package for proving q-hypergeometric multiple summation identities, 349 RIESE, A., qMultiSum-a package for proving q-hypergeometric multiple  ...  laws of syzygies, 499 YU, P. and YUAN, Y., A matching pursuit technique for computing the simplest normal forms of vector fields, 591 ZHANG, B-Y., A new elementary algorithm for proving q-hypergeometric  ... 
doi:10.1016/s0747-7171(03)00152-4 fatcat:gnptdsf7grf75aoiujuxvve46a

Author index to volume 296

2005 Discrete Mathematics  
Zeng, A short proof of the q-Dixon identity (2-3) 259-261 Hong, Y. and X.-D.  ...  Golumbic (1) 25-41 Ku¨ndgen, A. and M. Spangler, A bound on the total size of a cut cover (1) 121-128 Kyriakoussis, A. and M.G.  ... 
doi:10.1016/s0012-365x(05)00315-8 fatcat:m2gwquhb4zcw5h3uc4nmsxjc2u

349. The Polar Circle

W. Gallatly
1911 Mathematical Gazette  
I should be glad to meet with a short proof by Pure Geometry.] W. GALLATLY. foci S, S', and axes 2p, 2q, then 4R. Q= SA . S'A. 2. AH.  ...  I should be glad to meet with a short proof by Pure Geometry.] W. GALLATLY. 350. [Vol. v. p. 396.] I think that Mr.  ... 
doi:10.2307/3603254 fatcat:g4falfplhbgeveaxelkcny5xui

Gauss's 2F1(1) cannot be generalized to 2F1(x)

Doron Zeilberger
1992 Journal of Computational and Applied Mathematics  
A short proof of Wimp's theorem that asserts that 3Fz(a, b, c; d, e; 1) cannot be expressed in closed form is also given.  ...  Using ideas of Jet Wimp and Richard McIntosh, it is proved that Gauss's explicit evaluation of zFI(a, 6; c; 1) cannot be generalized to zFI(a, 6; c; x), for arbitrary a, b, c and X.  ...  •I A short proof of Wimp's theorem I will now give a short proof of Wimp's theorem [7] that ,F,(a, b, c; d, e; 1) cannot be expressed in closed form, in the form analogous to (7).  ... 
doi:10.1016/0377-0427(92)90211-f fatcat:gahmgjlmxfgrtlk5pd6rjzyuku

Page 3391 of Mathematical Reviews Vol. , Issue 86h [page]

1986 Mathematical Reviews  
A short algebraic proof is given for the identity S(n) = 3n(?"). A beautiful combinatorial interpretation of this result is given in terms of paths on lozenge- shaped and chevron-shaped lattices.  ...  The author gives bijective proofs-of the following results: (1) an explicit formula for HS, when \ = I*, (2) a factorization theorem for HS, when d contains /*, (3) a generalized Cauchy identity, (4) a  ... 

What can we do with a Solution?

Simon Langley, Daniel Richardson
2002 Electronical Notes in Theoretical Computer Science  
If S = 0 is a system of n equations and unknowns over C and S(α) = 0 to what extent can we compute with the point α?  ...  In particular, can we decide whether or not a polynomial expressions in the components of α with integral coefficients is zero?  ...  Sketch of proof Let α be a solution of a nonsingular set of elementary equations.  ... 
doi:10.1016/s1571-0661(04)80383-9 fatcat:qzycty6fizay5dl4e3bhnaomyq

Page 10 of Mathematical Reviews Vol. 29, Issue 1 [page]

1965 Mathematical Reviews  
A short new proof is given of the famous theorem that every positive integer can be written as the sum of four squares. W. H. Mills (Princeton, N.J.) Yahya, Q. A. M. M.  ...  Cohen (Knoxville, Tenn.) 52 (Spanish Carlitz, L. 53 A basic analog of the multinomial theorem. Scripta Math. 26, 317-321 (1963). The identities n-1 n TT G+pre) = 5 prema ar, r=0 r=0 r TH a-vey?  ... 

A short derivation of an elegant sum involving central binomial coefficients due to László via a hypergeometric series approach

Dongkyu Lim, Arjun K. Rathie
2022 Contributions to Mathematics  
The aim of this short note is to establish an elegant sum involving central binomial coefficients, due to L ászló [Amer. Math. Monthly 108 (2001) 851-855], via a hypergeometric series approach.  ...  Acknowledgement The work of Dongkyu Lim was partially supported by the National Research Foundation (NRF) of Korea through a grant funded by the Korean government (MSIT) NRF-2021R1C1C1010902.  ...  We recall that the generalized hypergeometric function with p numerator and q denominator parameters, in terms of the Pochhammer symbol, is p F q a 1 , . . . , a p b 1 , . . . , b q ; x = ∞ n=0 (a 1 )  ... 
doi:10.47443/cm.2022.025 doaj:9a20f482e43149419765ab700ce66764 fatcat:3bixiauy4nc5zjyu7k5vnsuldm

Cayley–Dixon projection operator for multi-univariate composed polynomials

Arthur D. Chtcherba, Deepak Kapur, Manfred Minimair
2009 Journal of symbolic computation  
Under some conditions, it is shown that a Dixon projection operator of the composed system can be expressed as a power of the resultant of the outer polynomial system multiplied by powers of the leading  ...  In this paper, the behavior of the Cayley-Dixon projection operator and the structure of Dixon matrices are analyzed for composed polynomial systems constructed from a multivariate system in which each  ...  Acknowledgements All the authors were supported by NSF grants, numbers CCF-0729097, CCR-0203051 and a grant from the Computer Science Research Institute at the Sandia National Labs.  ... 
doi:10.1016/j.jsc.2008.07.007 fatcat:j3j6vgvjtrdgpkg4wppl3sddam

Page 75 of Mathematical Reviews Vol. 48, Issue 1 [page]

1974 Mathematical Reviews  
points is not the identity and is semiregular on the remaining points; then n=p?+p and @ is either the alternating or the symmetric group. The proof is elementary. J. D. Dixon (Ottawa, Ont.)  ...  The object of this short note is the proof of the following theorem: Let p be an odd prime, and @ a p?-transitive permutation group of degree n; assume that the stabilizer in G of p?  ... 

An elliptic hypergeometric beta integral transformation [article]

Fokko J. van de Bult
2009 arXiv   pre-print
Moreover it gives a different proof of an identity in another article by Rains. We also give some basic hypergeometric and classical limits of this identity.  ...  The classical limit gives identities (some known, some new) between generalizations of the Selberg integral.  ...  A recent overview of these results is given in [11] . In this short article we prove a multivariate elliptic hypergeometric integral identity.  ... 
arXiv:0912.3812v1 fatcat:zwyre2y7onekhaovtujkqbikta

Page 310 of Mathematical Reviews Vol. 35, Issue 2 [page]

1968 Mathematical Reviews  
The author gives a short proof for the commutative case of a theorem (Schur, Zassenhaus) on complements in finite groups. {See also #1663 below.} 1662 H.  ...  These facts show that 2 is related to | a certain class $ of groups all having the form of a com- plete wreath product of an abelian p-group by a locally nil- | potent (p, q)-group, for some p, q.  ... 
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