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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=3, b1>=-23/4 > For fixed z and a1=3, b1=-19/4





http://functions.wolfram.com/07.22.03.6853.01









  


  










Input Form





HypergeometricPFQ[{3}, {-(19/4), 23/4}, -z] == (1/(16384 z^(19/4))) (4 z^(3/4) (-36010099125 + 8519682600 z - 832431600 z^2 + 35418240 z^3 - 609536 z^4 + 2048 z^5) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((108030297375 - 210753843300 z + 61491830400 z^2 - 6235669440 z^3 + 272067840 z^4 - 4776960 z^5 + 16384 z^6) Cos[2 Sqrt[z]] + 2 Sqrt[z] (108030297375 - 66713446800 z + 10951340400 z^2 - 721543680 z^3 + 20570880 z^4 - 192512 z^5) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-108030297375 + 66713446800 z - 10951340400 z^2 + 721543680 z^3 - 20570880 z^4 + 192512 z^5) Cos[2 Sqrt[z]] + (108030297375 - 210753843300 z + 61491830400 z^2 - 6235669440 z^3 + 272067840 z^4 - 4776960 z^5 + 16384 z^6) Sin[2 Sqrt[z]]))










Standard Form





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MathML Form







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</cn> <apply> <times /> <cn type='integer'> 210753843300 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 108030297375 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </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