Geodesic
On the binomial identities of Frisch and Klamkin
Journal of integer sequences, Tome 19 (2016) no. 7
In this paper we investigate two somewhat similar identities for sums of ratios of binomial coefficients. We give several proofs, and note that the identities all follow from a hypergeometric identity of Gauss. Inverse identities are also given.
Classification : 05A19, 11B65, 33C10
Keywords: binomial identity, hypergeometric series, Gauss hypergeometric summation formula, binomial inversion 
@article{JIS_2016__19_7_a3,
     author = {Gould,  H.W. and Quaintance,  Jocelyn},
     title = {On the binomial identities of {Frisch} and {Klamkin}},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {7},
     zbl = {1348.05028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a3/}
}
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Gould,  H.W.; Quaintance,  Jocelyn. On the binomial identities of Frisch and Klamkin. Journal of integer sequences, Tome 19 (2016) no. 7. http://geodesic.mathdoc.fr/item/JIS_2016__19_7_a3/