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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=-3/4, b>=a > For fixed z and a=-3/4, b=-3/4





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









  


  










Input Form





Hypergeometric2F1[-(3/4), -(3/4), 9/2, z] == (1/(2197845 Pi^(3/2) z^(7/2))) (112 (-8 (-90 + 639 z - 2214 z^2 + 7479 z^3 + 4426 z^4) EllipticE[(1/2) (1 - Sqrt[z])] + 8 (-90 + 639 z - 2214 z^2 + 7479 z^3 + 4426 z^4) EllipticE[(1/2) (1 + Sqrt[z])] + (-360 - 180 Sqrt[z] + 2556 z + 1263 z^(3/2) - 8856 z^2 - 4329 z^(5/2) + 29916 z^3 + 34261 z^(7/2) + 17704 z^4 + 9945 z^(9/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (360 - 180 Sqrt[z] - 2556 z + 1263 z^(3/2) + 8856 z^2 - 4329 z^(5/2) - 29916 z^3 + 34261 z^(7/2) - 17704 z^4 + 9945 z^(9/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)










Standard Form





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MathML Form







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</apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </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