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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=-3/2, a2>=-3/2 > For fixed z and a1=-3/2, a2=2, a3>=2 > For fixed z and a1=-3/2, a2=2, a3=2 > For fixed z and a1=-3/2, a2=2, a3=2, b1=5/2





http://functions.wolfram.com/07.27.03.ah6i.01









  


  








Input Form





HypergeometricPFQ[{-(3/2), 2, 2}, {5/2, 5/2}, -z] == (-144 Pi^2 + 528 Sqrt[z] + 216 Pi^2 z + 1744 z^(3/2) + 486 Pi^2 z^2 + 900 z^(5/2) + 225 Pi^2 z^3)/(4096 z^(3/2)) + (1/(1024 z (1 + z)^(9/2))) ((-144 + 9320 z - 28338 z^2 - 79413 z^3 - 106093 z^4 - 75753 z^5 - 28161 z^6 - 4290 z^7) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(1024 z (1 + z)^(9/2))) ((144 - 9320 z + 28338 z^2 + 79413 z^3 + 106093 z^4 + 75753 z^5 + 28161 z^6 + 4290 z^7) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (3 Sqrt[1 + z] (4 + 112 z + 75 z^2) Log[Sqrt[z] + Sqrt[1 + z]])/ (1024 z^(3/2)) + (1/(1024 z (1 + z)^(9/2))) ((144 - 9320 z + 28338 z^2 + 79413 z^3 + 106093 z^4 + 75753 z^5 + 28161 z^6 + 4290 z^7) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])]) + (9 (-16 + 24 z + 54 z^2 + 25 z^3) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (1024 z^(3/2)) + (9 (-16 + 24 z + 54 z^2 + 25 z^3) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(1024 z^(3/2)) - (9 (-16 + 24 z + 54 z^2 + 25 z^3) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/ (1024 z^(3/2))








Standard Form





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MathML Form







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type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1024 </cn> <ci> z </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4290 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 28161 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 75753 </cn> <apply> <power /> <ci> z </ci> 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<apply> <times /> <cn type='integer'> 54 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24 </cn> <ci> z </ci> </apply> <cn type='integer'> -16 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ln /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 25 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 54 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24 </cn> <ci> z </ci> </apply> <cn type='integer'> -16 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep 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Date Added to functions.wolfram.com (modification date)





2007-05-02