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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=-19/4, b>=a > For fixed z and a=-19/4, b=23/4





http://functions.wolfram.com/07.23.03.a9x7.01









  


  








Input Form





Hypergeometric2F1[-(19/4), 23/4, 6, -z] == (1/(38444150745 Pi z^5)) (16384 (1 + z)^(1/4) (2 (2048 - 4128 z + 10467 z^2 - 36260 z^3 + 222495 z^4 + 3718806 z^5 + 10758384 z^6 + 13257504 z^7 + 7637760 z^8 + 1697280 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (2048 - 4128 z + 10467 z^2 - 36260 z^3 + 222495 z^4 + 3718806 z^5 + 10758384 z^6 + 13257504 z^7 + 7637760 z^8 + 1697280 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (-2048 + 5664 z - 14955 z^2 + 48230 z^3 - 260715 z^4 + 1176084 z^5 + 9395568 z^6 + 17222400 z^7 + 12729600 z^8 + 3394560 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])]))








Standard Form





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MathML Form







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</cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14955 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5664 </cn> <ci> z </ci> </apply> <cn type='integer'> -2048 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </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