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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=9/4





http://functions.wolfram.com/07.23.03.9715.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 9/4, 1/2, z] == (1/(3315 Pi^(3/2))) ((32 Sqrt[z] (-3051 + 27327 z - 80380 z^2 + 107296 z^3 - 67584 z^4 + 16384 z^5) EllipticE[(1/2) (1 - Sqrt[z])] - 32 Sqrt[z] (-3051 + 27327 z - 80380 z^2 + 107296 z^3 - 67584 z^4 + 16384 z^5) EllipticE[(1/2) (1 + Sqrt[z])] + (3315 + 48816 Sqrt[z] - 61782 z - 437232 z^(3/2) + 235363 z^2 + 1286080 z^(5/2) - 363136 z^3 - 1716736 z^(7/2) + 251904 z^4 + 1081344 z^(9/2) - 65536 z^5 - 262144 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (3315 - 48816 Sqrt[z] - 61782 z + 437232 z^(3/2) + 235363 z^2 - 1286080 z^(5/2) - 363136 z^3 + 1716736 z^(7/2) + 251904 z^4 - 1081344 z^(9/2) - 65536 z^5 + 262144 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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/> <cn type='integer'> 235363 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 437232 </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'> 61782 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 48816 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 3315 </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