On two results contiguous to a quadratic transformation formula due to Gauss (Q2710501)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On two results contiguous to a quadratic transformation formula due to Gauss |
scientific article |
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12 December 2001
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Watsons summation theorem
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0.9066065
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0.8661473
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0.8591447
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0.85832393
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On two results contiguous to a quadratic transformation formula due to Gauss (English)
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In a paper by \textit{J. L. Lavoie}, \textit{F. Grondin}, and \textit{A. K. Rathie} [Indian J. Math. 34, No. 1, 23-32 (1992; Zbl 0793.33005)], some summation formulas for the Clausenian series \(_3F_2[a,b,c; {1\over 2}(a+b+1+i), 2c+j;1]\) were given. Using these results along with suitable series manipulations, the authors establish quadratic transformations of the two functions \((1-x)^{-2a}_2 F_1[a,b;2b \pm 1;\xi]\), where \(\xi=-4x/ (1-x)^2\). Each of them equals a linear combination of two \(_2F_1\)'s, both having variable \(x^2\). (Gauss' transformation involves \(_2F_1[a,b;2b; \xi])\).
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