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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`=1/2





http://functions.wolfram.com/07.22.03.8266.01









  


  










Input Form





HypergeometricPFQ[{-(23/4)}, {1/2, 9/4}, z] == (-4 z^(1/4) (-948702429675 - 1264936572900 Sqrt[z] - 20779168606560 z + 126806237873280 z^(3/2) + 23581062731520 z^2 - 104988649651200 z^(5/2) - 4172507136000 z^3 + 17289666035712 z^(7/2) + 211446595584 z^4 - 856201887744 z^(9/2) - 3529506816 z^5 + 14168358912 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (-948702429675 + 1264936572900 Sqrt[z] - 20779168606560 z - 126806237873280 z^(3/2) + 23581062731520 z^2 + 104988649651200 z^(5/2) - 4172507136000 z^3 - 17289666035712 z^(7/2) + 211446595584 z^4 + 856201887744 z^(9/2) - 3529506816 z^5 - 14168358912 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-948702429675 + 35418224041200 z - 566691584659200 z^2 + 431765016883200 z^3 - 69780204748800 z^4 + 3435333156864 z^5 - 56723767296 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-948702429675 + 35418224041200 z - 566691584659200 z^2 + 431765016883200 z^3 - 69780204748800 z^4 + 3435333156864 z^5 - 56723767296 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(441483547115520 z^(5/4))










Standard Form





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MathML Form







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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 67108864 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16777216 </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'> 14168358912 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3529506816 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 856201887744 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 211446595584 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> 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<times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 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'> 268435456 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 56723767296 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3435333156864 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 69780204748800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> 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Rule Form





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





2007-05-02