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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`=3/2





http://functions.wolfram.com/07.22.03.8884.01









  


  










Input Form





HypergeometricPFQ[{-(21/4)}, {3/2, 3/4}, z] == (1/(186065510400 Sqrt[z])) ((-4 (1603929600 - 20050329600 Sqrt[z] - 11677898925 z + 57147394500 z^(3/2) + 4527411840 z^2 - 19185949440 z^(5/2) - 390351360 z^3 + 1590220800 z^(7/2) + 9830400 z^4 - 39518208 z^(9/2) - 65536 z^5 + 262144 z^(11/2) + E^(4 Sqrt[z]) (-1603929600 - 20050329600 Sqrt[z] + 11677898925 z + 57147394500 z^(3/2) - 4527411840 z^2 - 19185949440 z^(5/2) + 390351360 z^3 + 1590220800 z^(7/2) - 9830400 z^4 - 39518208 z^(9/2) + 65536 z^5 + 262144 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (105411381075 - 240940299600 z + 77879692800 z^2 - 6390128640 z^3 + 158269440 z^4 - 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (-105411381075 + 240940299600 z - 77879692800 z^2 + 6390128640 z^3 - 158269440 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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<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> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1048576 </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'> 158269440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6390128640 </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'> 77879692800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 240940299600 </cn> <ci> z </ci> </apply> <cn type='integer'> -105411381075 </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> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02