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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=2, a3>=2 > For fixed z and a1=-5/2, a2=2, a3=2 > For fixed z and a1=-5/2, a2=2, a3=2, b1=1/2





http://functions.wolfram.com/07.27.03.ac8x.01









  


  










Input Form





HypergeometricPFQ[{-(5/2), 2, 2}, {1/2, 7/2}, -z] == (1/(32768 z^2)) (-11520 - 2880 z + 27904 z^2 + 10800 Pi^2 z^(5/2) + 80200 z^3 + 22500 Pi^2 z^(7/2) + 44100 z^4 + 11025 Pi^2 z^(9/2)) + (1/(16384 (1 + z)^(13/2))) ((128768 - 4884768 z - 6915192 z^2 - 25811998 z^3 - 44069142 z^4 - 48970995 z^5 - 35341980 z^6 - 16051320 z^7 - 4174830 z^8 - 474495 z^9) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(16384 (1 + z)^(13/2))) ((-128768 + 4884768 z + 6915192 z^2 + 25811998 z^3 + 44069142 z^4 + 48970995 z^5 + 35341980 z^6 + 16051320 z^7 + 4174830 z^8 + 474495 z^9) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (15 Sqrt[1 + z] (192 - 16 z + 112 z^2 + 1010 z^3 + 735 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/(8192 z^(5/2)) + (1/(16384 (1 + z)^(13/2))) ((-128768 + 4884768 z + 6915192 z^2 + 25811998 z^3 + 44069142 z^4 + 48970995 z^5 + 35341980 z^6 + 16051320 z^7 + 4174830 z^8 + 474495 z^9) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (225 Sqrt[z] (48 + 100 z + 49 z^2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/8192 + (225 Sqrt[z] (48 + 100 z + 49 z^2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/8192 - (225 Sqrt[z] (48 + 100 z + 49 z^2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/ 8192










Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 80200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10800 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 27904 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2880 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -11520 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 32768 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> 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type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 735 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1010 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 112 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 192 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> 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<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> </apply> <apply> <times /> <cn type='integer'> 225 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 49 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 100 </cn> <ci> z </ci> </apply> <cn type='integer'> 48 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> 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Date Added to functions.wolfram.com (modification date)





2007-05-02