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Generalization of a quadratic transformation due to Exton

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Y S Kim, A K Rathie, R B Paris

Classical Analysis and ODEs · Submitted 30 Mar 2014

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The authors' main claim We obtain the generalization of one of the Exton quadratic transformations.

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arXiv ID1403.7782 (version 1)
Pith IDCI4GDXQY, Pith's permanent record of this paper and its review
CitationA K Rathie, R B Paris, Y S Kim. "Generalization of a quadratic transformation due to Exton." arXiv:1403.7782 (2014). https://pith.science/paper/CI4GDXQY
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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.56 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; .

Exton [Ganita 54(2003)13-15] obtained numerous new quadratic transformations involving hypergeometric functions of order two and of higher order by applying various known classical summation theorems to a general transformation formula based on the Bailey transformation. We obtain the generalization of one of the Exton quadratic transformations. The results are derived with the help of a generalization of Dixon's summation theorem for the series ${}_3F_2$ obtained earlier by Lavoie {\em et al}. Several interesting known as well as new special cases and limiting cases are also given.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Exton [Ganita 54(2003)13-15] obtained numerous new quadratic transformations involving hypergeometric functions of order two and of higher order by applying various known classical summation theorems to a general transformation formula based on the Bailey transformation. background 1.00 0.04 0.05 asserted 1.00
s1 We obtain the generalization of one of the Exton quadratic transformations. contribution 0.97 0.96 0.81 asserted 1.00
s2 The results are derived with the help of a generalization of Dixon's summation theorem for the series ${}_3F_2$ obtained earlier by Lavoie {\em et al}. method 1.00 0.81 0.10 asserted 1.00
s3 Several interesting known as well as new special cases and limiting cases are also given. result 0.58 0.88 0.07 asserted 1.00

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Original abstract

Exton [Ganita 54(2003)13-15] obtained numerous new quadratic transformations involving hypergeometric functions of order two and of higher order by applying various known classical summation theorems to a general transformation formula based on the Bailey transformation. We obtain the generalization of one of the Exton quadratic transformations. The results are derived with the help of a generalization of Dixon's summation theorem for the series ${}_3F_2$ obtained earlier by Lavoie {\em et al}. Several interesting known as well as new special cases and limiting cases are also given.

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