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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=3 > For fixed z and a1=-3/2, a2=2, a3=3, b1=1/2





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









  


  








Input Form





HypergeometricPFQ[{-(3/2), 2, 3}, {1/2, 1/2}, -z] == (1/(256 (1 + z)^2)) (256 + 270 Pi^2 Sqrt[z] + 6092 z + 2115 Pi^2 z^(3/2) + 12280 z^2 + 3420 Pi^2 z^(5/2) + 6300 z^3 + 1575 Pi^2 z^(7/2)) + (1/(1024 (1 + z)^(11/2))) ((-1024 - 58336 z - 370224 z^2 - 1026760 z^3 - 1502896 z^4 - 1223487 z^5 - 526029 z^6 - 93480 z^7) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(1024 (1 + z)^(11/2))) ((1024 + 58336 z + 370224 z^2 + 1026760 z^3 + 1502896 z^4 + 1223487 z^5 + 526029 z^6 + 93480 z^7) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (3 (213 Sqrt[z] + 1015 z^(3/2) + 1315 z^(5/2) + 525 z^(7/2)) Log[Sqrt[z] + Sqrt[1 + z]])/(64 (1 + z)^(5/2)) + (1/(1024 (1 + z)^(11/2))) ((1024 + 58336 z + 370224 z^2 + 1026760 z^3 + 1502896 z^4 + 1223487 z^5 + 526029 z^6 + 93480 z^7) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (45/64) (6 Sqrt[z] + 35 z^(3/2)) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] + (45/64) (6 Sqrt[z] + 35 z^(3/2)) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] - (45/64) (6 Sqrt[z] + 35 z^(3/2)) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]








Standard Form





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MathML Form







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<cn type='integer'> 1026760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 370224 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 58336 </cn> <ci> z </ci> </apply> <cn type='integer'> 1024 </cn> </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> 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Date Added to functions.wolfram.com (modification date)





2007-05-02