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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=-15/4, b>=a > For fixed z and a=-15/4, b=21/4





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









  


  










Input Form





Hypergeometric2F1[-(15/4), 21/4, 3/2, z] == (1/(2197845 Pi^(3/2) Sqrt[z])) (2 (2 (266805 - 10189440 z + 58767360 z^2 - 105971712 z^3 + 58720256 z^4) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (266805 - 10189440 z + 58767360 z^2 - 105971712 z^3 + 58720256 z^4) EllipticE[(1/2) (1 + Sqrt[z])] - (266805 - 965520 Sqrt[z] - 10189440 z + 9477120 z^(3/2) + 58767360 z^2 - 22364160 z^(5/2) - 105971712 z^3 + 14680064 z^(7/2) + 58720256 z^4) EllipticK[(1/2) (1 - Sqrt[z])] + (266805 + 965520 Sqrt[z] - 10189440 z - 9477120 z^(3/2) + 58767360 z^2 + 22364160 z^(5/2) - 105971712 z^3 - 14680064 z^(7/2) + 58720256 z^4) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)










Standard Form





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MathML Form







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<times /> <cn type='integer'> 9477120 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10189440 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 965520 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 266805 </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