Abstract
ABSTRACTWe consider the hypergeometric function for . For , we derive a convergent expansion of in terms of the function and of rational functions of z that is uniformly valid for z in any compact in . When , the expansion also contains a logarithmic term of the form . For , we derive a convergent expansion of in terms of the function and of rational functions of z that is uniformly valid for z in any compact in in the exterior of the circle for arbitrary r>0. The expansions are accompanied by realistic error bounds. Some numerical experiments show the accuracy of the approximation.
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