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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=-15/4, b>=a > For fixed z and a=-15/4, b=13/4





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









  


  








Input Form





Hypergeometric2F1[-(15/4), 13/4, 4, -z] == (256 Sqrt[2] (Sqrt[1 + z] (2464 - 3465 z + 9702 z^2 + 152279 z^3 + 309888 z^4 + 239616 z^5 + 65536 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (2464 - 1001 z + 6237 z^2 + 161981 z^3 + 462167 z^4 + 549504 z^5 + 305152 z^6 + 65536 z^7) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - (2464 - 1617 z + 6930 z^2 + 53411 z^3 + 92208 z^4 + 64512 z^5 + 16384 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (2464 - 3465 z + 9702 z^2 + 152279 z^3 + 309888 z^4 + 239616 z^5 + 65536 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])]))/(13627845 Pi z^3 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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</cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3465 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 2464 </cn> </apply> <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> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02