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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 8 and fixed z and a<0 > For fixed z and a=-19/8, b>=a > For fixed z and a=-19/8, b=33/8





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









  


  










Input Form





Hypergeometric2F1[-(19/8), 33/8, 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (6848512 - 8801408 z - 3644333 z^2 - 3198118 z^3 - 5107333 z^4 + 78925280 z^5 - 96149760 z^6 + 33116160 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (6848512 - 11369600 z - 1046045 z^2 - 1302070 z^3 - 3299065 z^4 + 23500988 z^5 - 25589760 z^6 + 8279040 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (6848512 - 8801408 z - 3644333 z^2 - 3198118 z^3 - 5107333 z^4 + 78925280 z^5 - 96149760 z^6 + 33116160 z^7) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (6848512 - 8801408 z - 3644333 z^2 - 3198118 z^3 - 5107333 z^4 + 78925280 z^5 - 96149760 z^6 + 33116160 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (15204974763825 Pi (1 + Sqrt[1 - z])^(1/4) z^5)










Standard Form





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MathML Form







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type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5107333 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3198118 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3644333 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8801408 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 6848512 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> 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Rule Form





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





2007-05-02