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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=-1/2, a2>=-1/2 > For fixed z and a1=-1/2, a2=4, a3>=4 > For fixed z and a1=-1/2, a2=4, a3=4 > For fixed z and a1=-1/2, a2=4, a3=4, b1=1/2





http://functions.wolfram.com/07.27.03.am6n.01









  


  










Input Form





HypergeometricPFQ[{-(1/2), 4, 4}, {1/2, 3/2}, -z] == (1/(18432 (1 + z)^5)) (17532 + 11025 Pi^2 Sqrt[z] + 158628 z + 55125 Pi^2 z^(3/2) + 363640 z^2 + 110250 Pi^2 z^(5/2) + 396704 z^3 + 110250 Pi^2 z^(7/2) + 210700 z^4 + 55125 Pi^2 z^(9/2) + 44100 z^5 + 11025 Pi^2 z^(11/2)) + (1/(3072 (1 + z)^(13/2))) ((-3072 - 74058 z - 305322 z^2 - 629118 z^3 - 733122 z^4 - 495850 z^5 - 182360 z^6 - 28315 z^7) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(3072 (1 + z)^(13/2))) ((3072 + 74058 z + 305322 z^2 + 629118 z^3 + 733122 z^4 + 495850 z^5 + 182360 z^6 + 28315 z^7) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (5 (15 + 1444 z + 5377 z^2 + 9366 z^3 + 8477 z^4 + 3920 z^5 + 735 z^6) Log[Sqrt[z] + Sqrt[1 + z]])/(1536 Sqrt[z] (1 + z)^(11/2)) + (1/(3072 (1 + z)^(13/2))) ((3072 + 74058 z + 305322 z^2 + 629118 z^3 + 733122 z^4 + 495850 z^5 + 182360 z^6 + 28315 z^7) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (1225/512) Sqrt[z] Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] + (1225/512) Sqrt[z] PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] - (1225/512) Sqrt[z] PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]










Standard Form





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MathML Form







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type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1225 <sep /> 512 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </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> 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Date Added to functions.wolfram.com (modification date)





2007-05-02