Geodesic
Binomial sums via Bailey's cubic transformation
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1131-1150

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DOI Zbl

By employing one of the cubic transformations (due to W. N. Bailey (1928)) for the $_3F_2(x)$-series, we examine a class of $_3F_2(4)$-series. Several closed formulae are established by means of differentiation, integration and contiguous relations. As applications, some remarkable binomial sums are explicitly evaluated, including one proposed recently as an open problem.
By employing one of the cubic transformations (due to W. N. Bailey (1928)) for the $_3F_2(x)$-series, we examine a class of $_3F_2(4)$-series. Several closed formulae are established by means of differentiation, integration and contiguous relations. As applications, some remarkable binomial sums are explicitly evaluated, including one proposed recently as an open problem.
DOI : 10.21136/CMJ.2023.0429-22
Classification : 05A19, 11B65, 33C20
Keywords: hypergeometric series; Bailey's cubic transformation; contiguous relation; reversal series; binomial coefficient 
Chu, Wenchang. Binomial sums via Bailey's cubic transformation. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1131-1150. doi: 10.21136/CMJ.2023.0429-22
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