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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=-21/4, b>=a > For fixed z and a=-21/4, b=11/4





http://functions.wolfram.com/07.23.03.a8p9.01









  


  








Input Form





Hypergeometric2F1[-(21/4), 11/4, 6, z] == (1/(168441498225 Pi z^5)) (16384 (-2 (-452608 + 2581280 z - 4876807 z^2 + 1471860 z^3 + 2366910 z^4 - 28642268 z^5 + 57149265 z^6 - 57170112 z^7 + 32412160 z^8 - 9994240 z^9 + 1310720 z^10) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (452608 - 2468128 z + 4312815 z^2 - 649740 z^3 - 2181270 z^4 + 7664948 z^5 - 9774433 z^6 + 6500480 z^7 - 2263040 z^8 + 327680 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (-452608 + 2581280 z - 4876807 z^2 + 1471860 z^3 + 2366910 z^4 - 28642268 z^5 + 57149265 z^6 - 57170112 z^7 + 32412160 z^8 - 9994240 z^9 + 1310720 z^10) EllipticK[(1/2) (1 - Sqrt[1 - z])]))








Standard Form





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MathML Form







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<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> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02