Tricomi confluent hypergeometric function: Specific values (formula 07.33.03.0703)

HypergeometricU

$Mathematica Notation$

Hypergeometric Functions

HypergeometricU[a,b,z]

Specific values

For fixed z

For fixed z and a=9/2

http://functions.wolfram.com/07.33.03.0703.01

Input Form

HypergeometricU[9/2, -(9/2), -z] == (1/281302875) (4 (-z)^(11/2) (16899435/256 - (3246075 z)/32 + (2384235 z^2)/32 - 34965 z^3 + (48195 z^4)/4 - (6111 z^5)/2 + (945 z^6)/2 - 36 z^7 + z^8 + (1/(16384 z^6)) (((99225 + 2 z (99225 + 8 z (14175 + 2 z (6615 + z (6615 + 2 z (6615 + 4 z (-2205 + z (630 + z (-63 + 2 z))))))))) (945 Sqrt[Pi] Sqrt[-z] - 2 E^z z (945 + 2 z (-315 + 2 z (63 + 2 z (-9 + 2 z)))) + 945 Sqrt[Pi] Sqrt[z] Erfi[Sqrt[z]]))/E^z)))

Standard Form

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MathML Form

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type='integer'> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 34965 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2384235 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 32 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3246075 </cn> <ci> z </ci> <apply> <power /> <cn type='integer'> 32 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 16899435 <sep /> 256 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 16384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -63 </cn> </apply> </apply> <cn type='integer'> 630 </cn> </apply> </apply> <cn type='integer'> -2205 </cn> </apply> </apply> <cn type='integer'> 6615 </cn> </apply> </apply> <cn type='integer'> 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Rule Form

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

2007-05-02