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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=-9/4, b1`>=-11/2 > For fixed z and a1=-9/4, b1`=1/2





http://functions.wolfram.com/07.22.03.a9hw.01









  


  










Input Form





HypergeometricPFQ[{-(9/4)}, {1/2, 19/4}, z] == (1/(25769803776 z^(15/4))) ((11 (4 z^(1/4) (127702575 + 170270100 Sqrt[z] + 50485680 z - 36469440 z^(3/2) - 2419200 z^2 + 32901120 z^(5/2) - 38707200 z^3 + 215384064 z^(7/2) + 23789568 z^4 - 98304000 z^(9/2) - 1048576 z^5 + 4194304 z^(11/2) + E^(4 Sqrt[z]) (-127702575 + 170270100 Sqrt[z] - 50485680 z - 36469440 z^(3/2) + 2419200 z^2 + 32901120 z^(5/2) + 38707200 z^3 + 215384064 z^(7/2) - 23789568 z^4 - 98304000 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-127702575 + 85730400 z - 54432000 z^2 + 77414400 z^3 + 928972800 z^4 - 396361728 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-127702575 + 85730400 z - 54432000 z^2 + 77414400 z^3 + 928972800 z^4 - 396361728 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 396361728 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 928972800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 77414400 </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'> 54432000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 85730400 </cn> <ci> z </ci> </apply> <cn type='integer'> -127702575 </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> <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'> 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'> 396361728 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 928972800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 77414400 </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'> 54432000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 85730400 </cn> <ci> z </ci> </apply> <cn type='integer'> -127702575 </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