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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=-23/4, b>=a > For fixed z and a=-23/4, b=1/4





http://functions.wolfram.com/07.23.03.9475.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 1/4, 3, -z] == (64 Sqrt[2] (4 Sqrt[1 + z] (-24035 - 312455 z + 1344276 z^2 + 1065692 z^3 + 706175 z^4 + 318843 z^5 + 85504 z^6 + 10240 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 4 (-24035 - 336490 z + 1031821 z^2 + 2409968 z^3 + 1771867 z^4 + 1025018 z^5 + 404347 z^6 + 95744 z^7 + 10240 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 4 Sqrt[1 + z] (-24035 - 312455 z + 1344276 z^2 + 1065692 z^3 + 706175 z^4 + 318843 z^5 + 85504 z^6 + 10240 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-96140 - 1321925 z - 8755476 z^2 + 1229306 z^3 + 785624 z^4 + 341571 z^5 + 88384 z^6 + 10240 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (422463195 Pi z^2 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 422463195 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02