Rocky Mountain Journal of Mathematics

Note on the truncated generalizations of Gauss's square exponent theorem

Shane Chern

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In this note, we investigate Liu's work on the truncated Gaussian square exponent theorem and obtain more truncations. We also discuss some possible multiple summation extensions of Liu's results.

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Rocky Mountain J. Math., Volume 48, Number 7 (2018), 2211-2222.

First available in Project Euclid: 14 December 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11B65: Binomial coefficients; factorials; $q$-identities [See also 05A10, 05A30] 33D15: Basic hypergeometric functions in one variable, $_r\phi_s$

Gauss's square exponent theorem truncated identities multiple summations $q$-binomial coefficients


Chern, Shane. Note on the truncated generalizations of Gauss's square exponent theorem. Rocky Mountain J. Math. 48 (2018), no. 7, 2211--2222. doi:10.1216/RMJ-2018-48-7-2211.

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  • G.E. Andrews, The theory of partitions, Cambridge University Press, Cambridge, 1998.
  • G.E. Andrews and M. Merca, The truncated pentagonal number theorem, J. Combin. Th. 119 (2012), 1639–1643.
  • ––––, Truncated theta series and a problem of Guo and Zeng, J. Combin. Th. 154 (2018), 610–619.
  • A. Berkovich and F.G. Garvan, Some observations on Dyson's new symmetries of partitions, J. Combin. Th. 100 (2002), 61–93.
  • S.H. Chan, T.P.N. Ho and R. Mao, Truncated series from the quintuple product identity, J. Num. Th. 169 (2016), 420–438.
  • S.B. Ekhad and D. Zeilberger, The number of solutions of $X^2=0$ in triangular matrices over $GF(q)$, Electr. J. Combin. 3 (1996).
  • V.J.W. Guo and J. Zeng, Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas, Discr. Math. 308 (2008), 4069–4078.
  • ––––, Two truncated identities of Gauss, J. Combin. Th. 120 (2013), 700–707.
  • T.Y. He, K.Q. Ji and W.J.T. Zang, Bilateral truncated Jacobi's identity, European J. Combin. 51 (2016), 255–267.
  • F. Jouhet, Shifted versions of the Bailey and well-poised Bailey lemmas, Ramanujan J. 23 (2010), 315–333.
  • L.W. Kolitsch, Another approach to the truncated pentagonal number theorem, Int. J. Num. Th. 11 (2015), 1563–1569.
  • J.C. Liu, Some finite generalizations of Euler's pentagonal number theorem, Czechoslovak Math. J. 67 (2017), 525–531.
  • ––––, Some finite generalizations of Gauss's square exponent identity, Rocky Mountain J. Math. 47 (2017), 2723–2730.
  • R. Mao, Proofs of two conjectures on truncated series, J. Combin. Th. 130 (2015), 15–25.
  • A. Riese, qMultiSum–A package for proving $q$-hypergeometric multiple summation identities, J. Symbol. Comp. 35 (2003), 349–376.
  • S.O. Warnaar, $q$-Hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem, Ramanujan J. 8 (2004), 467–474.
  • A.J. Yee, A truncated Jacobi triple product theorem, J. Combin. Th. 130 (2015), 1–14.