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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=-17/4, b>=a > For fixed z and a=-17/4, b=15/4





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









  


  










Input Form





Hypergeometric2F1[-(17/4), 15/4, 5, z] == (1/(8549766225 Pi z^4)) (4096 (4 (42432 - 26520 z - 40443 z^2 - 147186 z^3 + 3106645 z^4 - 7995488 z^5 + 8759040 z^6 - 4538368 z^7 + 917504 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (-84864 + 31824 z + 78897 z^2 + 311610 z^3 - 1953515 z^4 + 3019136 z^5 - 1939456 z^6 + 458752 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] - 2 (42432 - 26520 z - 40443 z^2 - 147186 z^3 + 3106645 z^4 - 7995488 z^5 + 8759040 z^6 - 4538368 z^7 + 917504 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])]))










Standard Form





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MathML Form







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5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1953515 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 311610 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 78897 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 31824 </cn> <ci> z </ci> </apply> <cn type='integer'> -84864 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02