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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=-11/4





http://functions.wolfram.com/07.23.03.a94v.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(11/4), -(1/2), z] == (1/(390 Pi^(3/2))) ((2 Sqrt[z] (195 + 79467 z + 112557 z^2 + 4697 z^3 - 308 z^4) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (-195 - 79467 z - 112557 z^2 - 4697 z^3 + 308 z^4) EllipticE[(1/2) (1 + Sqrt[z])] + (390 - 195 Sqrt[z] - 10335 z - 79467 z^(3/2) - 105351 z^2 - 112557 z^(5/2) - 81389 z^3 - 4697 z^(7/2) + 77 z^4 + 308 z^(9/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (390 + 195 Sqrt[z] - 10335 z + 79467 z^(3/2) - 105351 z^2 + 112557 z^(5/2) - 81389 z^3 + 4697 z^(7/2) + 77 z^4 - 308 z^(9/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)










Standard Form





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MathML Form







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<ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 390 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </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