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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

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?
POSTED BY: Max Knoetig
3 Replies
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?
POSTED BY: Adam Domjan
Thanks, it helped!
POSTED BY: Max Knoetig
Try running this using higher precision calculations on HypergeometricU:
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 BY: Arnoud Buzing
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