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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=-21/4, b1`>=-11/2 > For fixed z and a1=-21/4, b1`=-1/2





http://functions.wolfram.com/07.22.03.8788.01









  


  










Input Form





HypergeometricPFQ[{-(21/4)}, {-(1/2), 3/4}, z] == (1/1703116800) ((4 (212889600 - 297868725 Sqrt[z] + 2441369700 z + 737936640 z^(3/2) - 3327448320 z^2 - 144990720 z^(5/2) + 598456320 z^3 + 6389760 z^(7/2) - 25755648 z^4 - 65536 z^(9/2) + 262144 z^5 + E^(4 Sqrt[z]) (212889600 + 297868725 Sqrt[z] + 2441369700 z - 737936640 z^(3/2) - 3327448320 z^2 + 144990720 z^(5/2) + 598456320 z^3 - 6389760 z^(7/2) - 25755648 z^4 + 65536 z^(9/2) + 262144 z^5)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (723647925 + 11578366800 z - 13722508800 z^2 + 2412748800 z^3 - 103219200 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (723647925 + 11578366800 z - 13722508800 z^2 + 2412748800 z^3 - 103219200 z^4 + 1048576 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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 103219200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2412748800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 13722508800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 11578366800 </cn> <ci> z </ci> </apply> <cn type='integer'> 723647925 </cn> </apply> <apply> <ci> Erf </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> 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<apply> <times /> <cn type='integer'> 11578366800 </cn> <ci> z </ci> </apply> <cn type='integer'> 723647925 </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> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02