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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/07.23.03.9736.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 9/4, 6, z] == (1/(551032827345 Pi z^5)) (16384 (-2 Sqrt[1 - z] (-894976 + 6111008 z - 15474607 z^2 + 12517428 z^3 + 15545838 z^4 - 81910108 z^5 + 126922761 z^6 - 107936064 z^7 + 54212096 z^8 - 15171584 z^9 + 1835008 z^10) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (-894976 + 6782240 z - 19994935 z^2 + 23722545 z^3 + 7066290 z^4 - 26793046 z^5 + 37843365 z^6 - 30342555 z^7 + 14560640 z^8 - 3921920 z^9 + 458752 z^10) EllipticK[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (-894976 + 6111008 z - 15474607 z^2 + 12517428 z^3 + 15545838 z^4 - 81910108 z^5 + 126922761 z^6 - 107936064 z^7 + 54212096 z^8 - 15171584 z^9 + 1835008 z^10) EllipticK[(1/2) (1 - Sqrt[1 - z])]))










Standard Form





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MathML Form







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<ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15474607 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6111008 </cn> <ci> z </ci> </apply> <cn type='integer'> -894976 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <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