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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.a9cl.01









  


  










Input Form





Hypergeometric2F1[-(19/4), 1/4, 1/2, z] == (1/(3315 Pi^(3/2))) ((-2 Sqrt[z] (9315 - 18630 z + 19267 z^2 - 9952 z^3 + 2048 z^4) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (9315 - 18630 z + 19267 z^2 - 9952 z^3 + 2048 z^4) EllipticE[(1/2) (1 + Sqrt[z])] + (3315 + 9315 Sqrt[z] - 3630 z - 18630 z^(3/2) + 4195 z^2 + 19267 z^(5/2) - 2344 z^3 - 9952 z^(7/2) + 512 z^4 + 2048 z^(9/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (3315 - 9315 Sqrt[z] - 3630 z + 18630 z^(3/2) + 4195 z^2 - 19267 z^(5/2) - 2344 z^3 + 9952 z^(7/2) + 512 z^4 - 2048 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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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