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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1},{b1,b2},z] > Specific values > For rational parameters with larger denominators and fixed z > For fixed z and a1=-23/4, b1`>=-11/2 > For fixed z and a1=-23/4, b1`=-11/2





http://functions.wolfram.com/07.22.03.7974.01









  


  










Input Form





HypergeometricPFQ[{-(23/4)}, {-(11/2), 5/4}, z] == (-4 z^(1/4) (330826228425 - 866892064500 Sqrt[z] + 70758530640 z - 246994816320 z^(3/2) + 8416074240 z^2 - 31488952320 z^(5/2) + 593141760 z^3 - 2277408768 z^(7/2) + 28114944 z^4 - 109314048 z^(9/2) + 1048576 z^5 - 4194304 z^(11/2) + E^(4 Sqrt[z]) (330826228425 + 866892064500 Sqrt[z] + 70758530640 z + 246994816320 z^(3/2) + 8416074240 z^2 + 31488952320 z^(5/2) + 593141760 z^3 + 2277408768 z^(7/2) + 28114944 z^4 + 109314048 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (2292816782025 + 3190005957600 z + 959400288000 z^2 + 124043673600 z^3 + 9021358080 z^4 + 434110464 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (2292816782025 + 3190005957600 z + 959400288000 z^2 + 124043673600 z^3 + 9021358080 z^4 + 434110464 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z])/(15695924428800 z^(1/4))










Standard Form





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MathML Form







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2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 16777216 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 434110464 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9021358080 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 124043673600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 959400288000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3190005957600 </cn> <ci> z </ci> </apply> <cn type='integer'> 2292816782025 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02