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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=-5/2, a2>=-5/2 > For fixed z and a1=-5/2, a2=3, a3>=3 > For fixed z and a1=-5/2, a2=3, a3=3 > For fixed z and a1=-5/2, a2=3, a3=3, b1=3/2





http://functions.wolfram.com/07.27.03.ad39.01









  


  










Input Form





HypergeometricPFQ[{-(5/2), 3, 3}, {3/2, 3/2}, -z] == (1/(65536 Sqrt[z])) (720 Pi^2 + 52336 Sqrt[z] + 27000 Pi^2 z + 352800 z^(3/2) + 110250 Pi^2 z^2 + 396900 z^(5/2) + 99225 Pi^2 z^3) + (1/(49152 (1 + z)^(11/2))) ((-46992 - 911256 z - 5451954 z^2 - 16404701 z^3 - 28634054 z^4 - 30445143 z^5 - 19525110 z^6 - 6964860 z^7 - 1064070 z^8) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(49152 (1 + z)^(11/2))) ((46992 + 911256 z + 5451954 z^2 + 16404701 z^3 + 28634054 z^4 + 30445143 z^5 + 19525110 z^6 + 6964860 z^7 + 1064070 z^8) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (15 (172 + 3368 z + 9555 z^2 + 6615 z^3) Log[Sqrt[z] + Sqrt[1 + z]])/ (16384 Sqrt[z] Sqrt[1 + z]) + (1/(49152 (1 + z)^(11/2))) ((46992 + 911256 z + 5451954 z^2 + 16404701 z^3 + 28634054 z^4 + 30445143 z^5 + 19525110 z^6 + 6964860 z^7 + 1064070 z^8) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (45 (16 + 600 z + 2450 z^2 + 2205 z^3) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (16384 Sqrt[z]) + (45 (16 + 600 z + 2450 z^2 + 2205 z^3) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(16384 Sqrt[z]) - (45 (16 + 600 z + 2450 z^2 + 2205 z^3) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/(16384 Sqrt[z])










Standard Form





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MathML Form







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<times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <cn type='integer'> 3 </cn> <cn type='integer'> 3 </cn> </list> <list> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 99225 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 396900 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 110250 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 352800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 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type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6964860 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19525110 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 30445143 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 28634054 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16404701 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5451954 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 911256 </cn> <ci> z </ci> </apply> <cn type='integer'> 46992 </cn> </apply> <apply> <ln /> <apply> <times /> <apply> <plus /> <apply> <power 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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'> 16384 </cn> <apply> 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Date Added to functions.wolfram.com (modification date)





2007-05-02