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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=9/4





http://functions.wolfram.com/07.23.03.9729.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 9/4, 4, -z] == (256 Sqrt[2] (Sqrt[1 + z] (-153824 - 418209 z + 706629 z^2 + 7657949 z^3 + 18131415 z^4 + 21657408 z^5 + 14499328 z^6 + 5210112 z^7 + 786432 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-153824 - 572033 z + 288420 z^2 + 8364578 z^3 + 25789364 z^4 + 39788823 z^5 + 36156736 z^6 + 19709440 z^7 + 5996544 z^8 + 786432 z^9) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-153824 - 533577 z + 403788 z^2 + 2711546 z^3 + 5679180 z^4 + 6281223 z^5 + 3965824 z^6 + 1357824 z^7 + 196608 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-153824 - 418209 z + 706629 z^2 + 7657949 z^3 + 18131415 z^4 + 21657408 z^5 + 14499328 z^6 + 5210112 z^7 + 786432 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (704105325 Pi z^3 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 786432 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5210112 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 14499328 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21657408 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 18131415 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7657949 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 706629 </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'> 418209 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -153824 </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> <power /> <apply> <times /> <cn type='integer'> 704105325 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </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