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# Calculation of the confluent hypergeometric function HypergeometricU

Posted 11 years ago
 Dear Colleagues,I am currently studying, in particular, the HypergeometricU function (confluent hypergeometric function) for a statistics problem. (using Mathematica 9.0.1.0)Unfortunately, Mathematica seems to be able to calculate the function only with gaps, in the regions where I would like to evaluate it. See for example: LogPlot[HypergeometricU[10.5, 31, x], {x, 0, 300}]Is there a way of calculating the function values within such gaps?
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Posted 11 years ago
 Try running this using higher precision calculations on HypergeometricU:ListLogPlot[ Table[{x, N[HypergeometricU[21/2, 31, x], 50]}, {x, 1, 300, 1}], Joined -> True]The behavior you are observing (the gap in the plot) looks like a deficiency in the HypergeometricU computation at machine precision. I've asked our developers to look into the issue.
Posted 11 years ago
 Thanks, it helped!
Posted 11 years ago
 Dear Wolfram Community!I have got the following problem, but the listlogplot method does not help me.I have got the following functions: f[s_]:=HypergeometricU[ 1/2+i*2*s , 1, i*14*s ];This function's value is not good for s>4:Plot[ Re[ f ], {s,3,6}, PlotRange->All,PlotStyle->Thick ]:or ListLogPlot[ Table[ {s,N[ Re[ f ] ,50] } ], {s, 3, 6, 0.05} , Joined->True, PlotRange->All ]The $MaxExtraPrecision Command also does not do anything.Block[{$MaxExtraPrecision = 1000},  ListPlot[ Table[ {s, N[Re[ f ], 500] }, {s, 3, 6, 0.05} ], Joined -> True, PlotRange -> All ] ]How can i improve the calculation of my function for s>4?