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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-19/4, b>=a > For fixed z and a=-19/4, b=1/4





http://functions.wolfram.com/07.23.03.a9cr.01









  


  










Input Form





Hypergeometric2F1[-(19/4), 1/4, 2, -z] == (1/(504735 Pi z Sqrt[1 + Sqrt[1 + z]])) (8 Sqrt[2] (Sqrt[1 + z] (-7315 + 59181 z + 53283 z^2 + 34531 z^3 + 12832 z^4 + 2048 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-7315 + 51866 z + 112464 z^2 + 87814 z^3 + 47363 z^4 + 14880 z^5 + 2048 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-7315 - 72489 z + 15375 z^2 + 9469 z^3 + 3352 z^4 + 512 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-7315 + 59181 z + 53283 z^2 + 34531 z^3 + 12832 z^4 + 2048 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))










Standard Form





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MathML Form







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<ci> z </ci> </apply> <cn type='integer'> -7315 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </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