Rothe–Hagen identity

In mathematics, the Rothe–Hagen identity is a mathematical identity valid for all complex numbers () except where its denominators vanish:

It is a generalization of Vandermonde's identity, and is named after Heinrich August Rothe and Johann Georg Hagen.

References

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  • Chu, Wenchang (2010), "Elementary proofs for convolution identities of Abel and Hagen-Rothe", Electronic Journal of Combinatorics, 17 (1), N24, doi:10.37236/473.
  • Gould, H. W. (1956), "Some generalizations of Vandermonde's convolution", The American Mathematical Monthly, 63 (2): 84–91, doi:10.1080/00029890.1956.11988763, JSTOR 2306429, MR 0075170. See especially pp. 89–91.
  • Hagen, Johann G. (1891), Synopsis Der Hoeheren Mathematik, Berlin, formula 17, pp. 64–68, vol. I{{citation}}: CS1 maint: location missing publisher (link). As cited by Gould (1956).
  • Ma, Xinrong (2011), "Two matrix inversions associated with the Hagen-Rothe formula, their q-analogues and applications", Journal of Combinatorial Theory, Series A, 118 (4): 1475–1493, doi:10.1016/j.jcta.2010.12.012, MR 2763069.
  • Rothe, Heinrich August (1793), Formulae De Serierum Reversione Demonstratio Universalis Signis Localibus Combinatorio-Analyticorum Vicariis Exhibita: Dissertatio Academica, Leipzig. As cited by Gould (1956).