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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=2, b1>=-23/4 > For fixed z and a1=2, b1=-19/4





http://functions.wolfram.com/07.22.03.6562.01









  


  










Input Form





HypergeometricPFQ[{2}, {-(19/4), 23/4}, z] == (1/(8192 z^(19/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (3273645375 + 682624800 z + 56300400 z^2 + 1647360 z^3 + 13568 z^4) - E^(4 Sqrt[z]) Sqrt[2 Pi] (-9820936125 + 19641872250 Sqrt[z] - 18883764900 z + 11578366800 z^(3/2) - 5059454400 z^2 + 1664863200 z^(5/2) - 423783360 z^3 + 84015360 z^(7/2) - 12798720 z^4 + 1436160 z^(9/2) - 107520 z^5 + 4096 z^(11/2)) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (9820936125 + 19641872250 Sqrt[z] + 18883764900 z + 11578366800 z^(3/2) + 5059454400 z^2 + 1664863200 z^(5/2) + 423783360 z^3 + 84015360 z^(7/2) + 12798720 z^4 + 1436160 z^(9/2) + 107520 z^5 + 4096 z^(11/2)) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))










Standard Form





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MathML Form







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<power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11578366800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 18883764900 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 19641872250 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 9820936125 </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