Abstract
From Goursat"s transformation formulas for the hypergeometric function $F(\alpha,\beta,\gamma;z)$, we derive several double sequences given by mean iterations and express their common limits by the hypergeometric function. Our results are analogies of the fact that the arithmetic-geometric mean of 1 and $x\in (0,1)$ can be expressed as the reciprocal of $F \big( {1\over2},{1\over2},1;1-x^2 \big)$.
Citation
Ryohei HATTORI. Takayuki KATO. Keiji MATSUMOTO. "Mean iterations derived from transformation formulas for the hypergeometric function." Hokkaido Math. J. 38 (3) 563 - 586, August 2009. https://doi.org/10.14492/hokmj/1258553977
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