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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=6, b1>=-23/4 > For fixed z and a1=6, b1=-17/4





http://functions.wolfram.com/07.22.03.7742.01









  


  










Input Form





HypergeometricPFQ[{6}, {-(17/4), 21/4}, z] == (1/(125829120 z^(17/4))) ((24 E^(2 Sqrt[z]) z^(1/4) (-20158763625 - 9340531200 z - 2108106000 z^2 - 290062080 z^3 - 38954240 z^4 - 4874240 z^5 + 65536 z^6) - E^(4 Sqrt[z]) Sqrt[2 Pi] (-60476290875 + 120952581750 Sqrt[z] - 124783659000 z + 88297209000 z^(3/2) - 48291843600 z^2 + 21859437600 z^(5/2) - 8602070400 z^3 + 3069792000 z^(7/2) - 1070150400 z^4 + 412853760 z^(9/2) - 169973760 z^5 + 56279040 z^(11/2) - 9830400 z^6 - 655360 z^(13/2) + 524288 z^7) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (60476290875 + 120952581750 Sqrt[z] + 124783659000 z + 88297209000 z^(3/2) + 48291843600 z^2 + 21859437600 z^(5/2) + 8602070400 z^3 + 3069792000 z^(7/2) + 1070150400 z^4 + 412853760 z^(9/2) + 169973760 z^5 + 56279040 z^(11/2) + 9830400 z^6 - 655360 z^(13/2) - 524288 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))










Standard Form





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MathML Form







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<plus /> <apply> <times /> <cn type='integer'> -524288 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 655360 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9830400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 56279040 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 169973760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 412853760 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1070150400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3069792000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8602070400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21859437600 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 48291843600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 88297209000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 124783659000 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 120952581750 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 60476290875 </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