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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=-23/4, b>=a > For fixed z and a=-23/4, b=13/4





http://functions.wolfram.com/07.23.03.9843.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 13/4, 1/2, z] == (1/(29835 Pi^(3/2))) ((2 Sqrt[z] (-540291 + 6665763 z - 25000832 z^2 + 40568832 z^3 - 30081024 z^4 + 8388608 z^5) EllipticE[(1/2) (1 - Sqrt[z])] - 2 Sqrt[z] (-540291 + 6665763 z - 25000832 z^2 + 40568832 z^3 - 30081024 z^4 + 8388608 z^5) EllipticE[(1/2) (1 + Sqrt[z])] + (29835 + 540291 Sqrt[z] - 848667 z - 6665763 z^(3/2) + 4331120 z^2 + 25000832 z^(5/2) - 8346624 z^3 - 40568832 z^(7/2) + 6930432 z^4 + 30081024 z^(9/2) - 2097152 z^5 - 8388608 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (29835 - 540291 Sqrt[z] - 848667 z + 6665763 z^(3/2) + 4331120 z^2 - 25000832 z^(5/2) - 8346624 z^3 + 40568832 z^(7/2) + 6930432 z^4 - 30081024 z^(9/2) - 2097152 z^5 + 8388608 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)










Standard Form





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MathML Form







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<power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4331120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6665763 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 848667 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 540291 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 29835 </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