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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 5 and fixed z > For fixed z and a=-1/5, b>=a > For fixed z and a=-1/5, b=5





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









  


  










Input Form





Hypergeometric2F1[-(1/5), 5, 19/5, z] == -((1/(390625 (-1 + z) z^(14/5))) (21 (-1)^(1/5) (12 (-1)^(4/5) (3 + 8 z + 33 z^2 - 352 z^3 + 308 z^4) Log[1 - z^(1/5)] + 12 (3 + 8 z + 33 z^2 - 352 z^3 + 308 z^4) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-12 (3 + 8 z + 33 z^2 - 352 z^3 + 308 z^4) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (12 (3 + 8 z + 33 z^2 - 352 z^3 + 308 z^4) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (9 + 28 z - 3608 z^2 + 3696 z^3) - 12 (3 + 8 z + 33 z^2 - 352 z^3 + 308 z^4) Log[1 - (-1)^(4/5) z^(1/5)]))))))










Standard Form





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MathML Form







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</apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 308 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 352 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 33 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </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