Geodesic
Reciprocal Formulae on Binomial Convolutions of Hagen-Rothe Type
Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 591-605
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By means of duplicate inverse series relations, we investigate dual relations of four binomial convolution identities. Four classes of reciprocal formulae on binomial convolutions of Hagen-Rothe type are established. They reflect certain “reciprocity” on the Hagen-Rothe-like convolutions in the sense that each binomial summation involved has no closed form in general, but their sum and difference in pairs do have simple expressions in a single term of binomial coefficients. 
@article{BUMI_2013_9_6_3_a6,
     author = {Chu, Wenchang},
     title = {Reciprocal {Formulae} on {Binomial} {Convolutions} of {Hagen-Rothe} {Type}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {591--605},
     year = {2013},
     volume = {Ser. 9, 6},
     number = {3},
     mrnumber = {3202842},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a6/}
}
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Chu, Wenchang. Reciprocal Formulae on Binomial Convolutions of Hagen-Rothe Type. Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 591-605. http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a6/