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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=-7/4, b>=a > For fixed z and a=-7/4, b=21/4





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









  


  










Input Form





Hypergeometric2F1[-(7/4), 21/4, 7/2, z] == (1/(2197845 Pi^(3/2) z^(5/2))) (8 (2 (1764 + 13965 z + 169344 z^2 - 1034240 z^3 + 983040 z^4) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (1764 + 13965 z + 169344 z^2 - 1034240 z^3 + 983040 z^4) EllipticE[(1/2) (1 + Sqrt[z])] - (1764 + 882 Sqrt[z] + 13965 z + 7056 z^(3/2) + 169344 z^2 - 189440 z^(5/2) - 1034240 z^3 + 245760 z^(7/2) + 983040 z^4) EllipticK[(1/2) (1 - Sqrt[z])] + (1764 - 882 Sqrt[z] + 13965 z - 7056 z^(3/2) + 169344 z^2 + 189440 z^(5/2) - 1034240 z^3 - 245760 z^(7/2) + 983040 z^4) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)










Standard Form





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MathML Form







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type='integer'> 882 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 1764 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </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