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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=-7/2, a2>=-7/2 > For fixed z and a1=-7/2, a2=-7/2, a3>=-7/2 > For fixed z and a1=-7/2, a2=-7/2, a3=-7/2 > For fixed z and a1=-7/2, a2=-7/2, a3=-7/2, b1=7/2





http://functions.wolfram.com/07.27.03.1042.01









  


  










Input Form





HypergeometricPFQ[{-(7/2), -(7/2), -(7/2)}, {7/2, 7/2}, z] == (1/(25769803776 z^2)) (Sqrt[1 - z] (-687715 - 72300970 z + 20862818336 z^2 - 56232956768 z^3 + 15065207488 z^4 - 285140096 z^5)) + (1225 (7 Pi^2 + 1008 Pi^2 z + 63000 Pi^2 z^2 - 896000 Pi^2 z^3 + 1008000 Pi^2 z^4 - 129024 Pi^2 z^5 + 1024 Pi^2 z^6))/ (12884901888 (-z)^(5/2)) - (1/(25769803776 (-z)^(5/2))) (35 (-13769 - 1206576 z - 85995000 z^2 - 62720000 z^3 + 987840000 z^4 - 251080704 z^5 + 3549184 z^6) Log[Sqrt[1 - z] + Sqrt[-z]]) - (1/(2147483648 (-z)^(5/2))) (1225 (7 + 1008 z + 63000 z^2 - 896000 z^3 + 1008000 z^4 - 129024 z^5 + 1024 z^6) Log[Sqrt[1 - z] + Sqrt[-z]]^2) + (1/(1073741824 (-z)^(5/2))) (1225 (7 + 1008 z + 63000 z^2 - 896000 z^3 + 1008000 z^4 - 129024 z^5 + 1024 z^6) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]]) + (1/(1073741824 (-z)^(5/2))) (1225 (7 + 1008 z + 63000 z^2 - 896000 z^3 + 1008000 z^4 - 129024 z^5 + 1024 z^6) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]]) - (1/(1073741824 (-z)^(5/2))) (1225 (7 + 1008 z + 63000 z^2 - 896000 z^3 + 1008000 z^4 - 129024 z^5 + 1024 z^6) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </list> <list> <cn type='rational'> 7 <sep /> 2 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2147483648 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1225 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 129024 </cn> 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</apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </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'> 25769803776 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3549184 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 251080704 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 987840000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn 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<apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1073741824 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1225 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 129024 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1008000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 896000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 63000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1008 </cn> <ci> z </ci> </apply> <cn type='integer'> 7 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </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'> 1073741824 </cn> <apply> <power /> <apply> <times /> 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Date Added to functions.wolfram.com (modification date)





2007-05-02