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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=-29/8, b>=a > For fixed z and a=-29/8, b=17/8





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









  


  










Input Form





Hypergeometric2F1[-(29/8), 17/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (-12353536 + 69826432 z - 145746315 z^2 + 104095355 z^3 + 74353825 z^4 - 258939543 z^5 + 234698486 z^6 - 97900880 z^7 + 16151520 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-12353536 + 69826432 z - 145746315 z^2 + 104095355 z^3 + 74353825 z^4 - 258939543 z^5 + 234698486 z^6 - 97900880 z^7 + 16151520 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-12353536 + 77547392 z - 188121115 z^2 + 188620640 z^3 + 21243950 z^4 - 52873228 z^5 + 43620581 z^6 - 17117980 z^7 + 2691920 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-12353536 + 69826432 z - 145746315 z^2 + 104095355 z^3 + 74353825 z^4 - 258939543 z^5 + 234698486 z^6 - 97900880 z^7 + 16151520 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/(67632822821655 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^5)










Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 69826432 </cn> <ci> z </ci> </apply> <cn type='integer'> -12353536 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <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> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> 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<apply> <times /> <cn type='integer'> 188121115 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 77547392 </cn> <ci> z </ci> </apply> <cn type='integer'> -12353536 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <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> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 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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> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 67632822821655 </cn> <pi /> <apply> <power /> <apply> <plus /> <apply> <power /> <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> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> 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Rule Form





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





2007-05-02