Abstract
It is well known that inversion techniques have an important role in the development of combinatorial identities. In 1973, Gould and Hsu [6] offered a pair of surprising inverse series relations. Then it was utilized by Chu [3, 4] to study systematically hypergeometric series identities. By applying the duplicate form of Gould-Hsu inversions to a terminating 4 F 3 −series identity form Saalscütz’s theorem, we shall establish a family of binomial identities implying numerous interesting hypergeometric series identities.
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References
Andrews, G.E., Askey, R., Roy, R.: Special Functions. Cambridge University Press, Cambridge (2000)
Bailey, W.N.: Generalized Hypergeometric Series. Cambridge University Press, Cambridge (1935)
Chu, W.: Inversion techniques and combinatorial identities. Boll. Un. Mat. Ital. B-7, 737–760 (1993)
Chu, W.: Inversion techniques and combinatorial identities: Strange evaluations of basic hypergeometric series. Compositio Math. 91, 121–144 (1994)
Chu, W., Wei, C.: Lengendre inversions and balanced hypergeometric series identities. Discrete Math. 308, 541–549 (2008)
Gould, H.W., Hsu, L.C.: Some new inverse series relations. Duke Math. J. 40, 885–891 (1973)
Ma, X.: An extension of Warnaar’s matrix inversion. Proc. Amer. Math. Soc. 133, 3179–3189 (2005)
Riordan, J.: Combinatorial Identities. John Wiley & Sons, Inc., New York (1968)
Warnaar, S.O.: Summation and transformation formulas for elliptic hypergeometric series. Constr. Approx. 18, 479–502 (2002)
Wei, C.: Applications of Inversions Techniques in Combnatorial Identities. Dalian University of Technology, Dalian (2006) (in Chinese)
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Wei, C., Gong, D., Li, J. (2011). Duplicate Form of Gould-Hsu Inversions and Binomial Identities. In: Liu, B., Chai, C. (eds) Information Computing and Applications. ICICA 2011. Lecture Notes in Computer Science, vol 7030. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25255-6_19
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DOI: https://doi.org/10.1007/978-3-642-25255-6_19
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