Tricomi confluent hypergeometric function: Specific values (formula 07.33.03.0423)

HypergeometricU

$Mathematica Notation$

Hypergeometric Functions

HypergeometricU[a,b,z]

Specific values

For fixed z

For fixed z and a=3/2

http://functions.wolfram.com/07.33.03.0423.01

Input Form

HypergeometricU[3/2, -4, -z] == -((1/(10395 Sqrt[Pi])) ((8 z (z (-24 + z (-21 + 4 z (-3 + z (-7 + 2 z)))) BesselK[0, z/2] + (-96 + z (-84 + z (-51 + 4 z (1 + z) (-7 + 2 z)))) BesselK[1, z/2] - (z (-24 + z (-21 + 4 z (-3 + z (-7 + 2 z)))) BesselI[0, z/2] + (96 + z (84 + z (51 + 4 z (7 + (5 - 2 z) z)))) BesselI[1, z/2]) (Log[-z] - Log[z])))/E^(z/2)))

Standard Form

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MathML Form

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<mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='integer'> -4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 10395 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <exponentiale /> <apply> 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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02