# Calculation of the confluent hypergeometric function HypergeometricU

Posted 10 years ago
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 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 9 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?
Posted 10 years ago
 Thanks, it helped!
Posted 10 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.