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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=7/2, b>=a > For fixed z and a=7/2, b=15/4





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









  


  








Input Form





Hypergeometric2F1[7/2, 15/4, 1, z] == (-26 (1 - z)^(3/2) (316 + 1136 z + 333 z^2) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 26 (-1 + z) (316 + 1136 z + 333 z^2) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 13 (1 - z)^(5/4) (316 + 1136 z + 333 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 13 (1 - z)^(3/2) (316 + 1136 z + 333 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 13 (-1 + z) (316 + 1136 z + 333 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-1028 + 8076 z + 14557 z^2 + 1600 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (770 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^7)








Standard Form





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MathML Form







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type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 5 <sep /> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 1600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 14557 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8076 </cn> <ci> z </ci> </apply> <cn type='integer'> -1028 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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 /> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 26 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 333 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1136 </cn> <ci> z </ci> </apply> <cn type='integer'> 316 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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 /> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 13 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 333 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1136 </cn> <ci> z </ci> </apply> <cn type='integer'> 316 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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 /> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 770 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <pi /> <apply> <power /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 7 </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