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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=5, b1>=-23/4 > For fixed z and a1=5, b1=-19/4





http://functions.wolfram.com/07.22.03.7421.01









  


  










Input Form





HypergeometricPFQ[{5}, {-(19/4), -(1/4)}, -z] == (1/790020) (4 (197505 - 831600 z + 574875 z^2 + 312480 z^3 + 60576 z^4 - 512 z^5) - Sqrt[Pi] z^(5/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((4385745 - 5290740 z - 2484720 z^2 - 505344 z^3 + 4096 z^4) Cos[2 Sqrt[z]] + 42 Sqrt[z] (208845 + 26520 z - 8704 z^2 + 2048 z^3) Sin[2 Sqrt[z]]) + Sqrt[Pi] z^(5/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (-42 Sqrt[z] (208845 + 26520 z - 8704 z^2 + 2048 z^3) Cos[2 Sqrt[z]] + (4385745 - 5290740 z - 2484720 z^2 - 505344 z^3 + 4096 z^4) Sin[2 Sqrt[z]]))










Standard Form





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MathML Form







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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5290740 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 4385745 </cn> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 42 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2048 </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'> 8704 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 26520 </cn> <ci> z </ci> </apply> <cn type='integer'> 208845 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 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Rule Form





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





2007-05-02