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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, b1>=-23/4 > For fixed z and a1=3, b1=-15/4





http://functions.wolfram.com/07.22.03.6890.01









  


  










Input Form





HypergeometricPFQ[{3}, {-(15/4), 19/4}, z] == (1/(16384 z^(15/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (52026975 + 12972960 z + 1330560 z^2 + 56320 z^3 + 512 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (156080925 - 312161850 Sqrt[z] + 306486180 z - 196756560 z^(3/2) + 92640240 z^2 - 33929280 z^(5/2) + 9959040 z^3 - 2354688 z^(7/2) + 435456 z^4 - 57344 z^(9/2) + 4096 z^5) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (156080925 + 312161850 Sqrt[z] + 306486180 z + 196756560 z^(3/2) + 92640240 z^2 + 33929280 z^(5/2) + 9959040 z^3 + 2354688 z^(7/2) + 435456 z^4 + 57344 z^(9/2) + 4096 z^5) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))










Standard Form





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MathML Form







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</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> <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'> 4096 </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'> 57344 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 435456 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2354688 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> 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Rule Form





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





2007-05-02