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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=3/4, b1`>=-11/2 > For fixed z and a1=3/4, b1`=9/2





http://functions.wolfram.com/07.22.03.acba.01









  


  










Input Form





HypergeometricPFQ[{3/4}, {9/2, 23/4}, z] == -((1/(268435456 z^(19/4))) ((9975 (4 z^(1/4) (800415 + 1067220 Sqrt[z] - 202032 z + 652992 z^(3/2) - 37632 z^2 + 138240 z^(5/2) - 4096 z^3 + 16384 z^(7/2) + E^(4 Sqrt[z]) (-800415 + 1067220 Sqrt[z] + 202032 z + 652992 z^(3/2) + 37632 z^2 + 138240 z^(5/2) + 4096 z^3 + 16384 z^(7/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-800415 + 3415104 z + 2483712 z^2 + 540672 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-800415 + 3415104 z + 2483712 z^2 + 540672 z^3 + 65536 z^4) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])))










Standard Form





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MathML Form







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z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 202032 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 1067220 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 16384 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4096 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 138240 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 37632 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 652992 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 202032 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 1067220 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -800415 </cn> </apply> </apply> <cn type='integer'> 800415 </cn> </apply> </apply> <apply> <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'> 65536 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> 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Rule Form





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





2007-05-02