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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=-17/4, b>=a > For fixed z and a=-17/4, b=-13/4





http://functions.wolfram.com/07.23.03.aa9l.01









  


  








Input Form





Hypergeometric2F1[-(17/4), -(13/4), 3, -z] == (64 Sqrt[2] ((-156 - 5109 z + 562215 z^2 - 2107570 z^3 + 1589650 z^4 - 229129 z^5 + 819 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (-156 - 5109 z + 562215 z^2 - 2107570 z^3 + 1589650 z^4 - 229129 z^5 + 819 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 Sqrt[1 + z] (78 + 2535 z - 167520 z^2 + 548690 z^3 - 361510 z^4 + 43407 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-156 - 5109 z + 562215 z^2 - 2107570 z^3 + 1589650 z^4 - 229129 z^5 + 819 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (7309575 Pi z^2 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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</apply> <apply> <times /> <cn type='integer'> 562215 </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'> 5109 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -156 </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