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Mean iterations derived from transformation formulas for the hypergeometric function

Ryohei HATTORI, Takayuki KATO, Keiji MATSUMOTO
2009 Hokkaido Mathematical Journal  
From Goursat's transformation formulas for the hypergeometric function F (α, β, γ; 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 arithmeticgeometric mean of 1 and x ∈ (0, 1) can be expressed as the reciprocal of F ( 1 2 , 1 2 , 1; 1 − x 2 ).
doi:10.14492/hokmj/1258553977 fatcat:q2velauu4ba2hi23der6izosgi