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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=17/4





http://functions.wolfram.com/07.23.03.agx1.01









  


  










Input Form





Hypergeometric2F1[-(3/4), 17/4, -(7/2), z] == (1/(109200 Pi^(3/2))) (((1/(-1 + z)^7) (2 Sqrt[z] (-54600 + 312000 z - 673335 z^2 + 525525 z^3 - 2630397 z^4 + 2343495 z^5 - 963424 z^6 + 157696 z^7) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^7) (2 Sqrt[z] (-54600 + 312000 z - 673335 z^2 + 525525 z^3 - 2630397 z^4 + 2343495 z^5 - 963424 z^6 + 157696 z^7) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((-109200 + 163800 Sqrt[z] + 542100 z - 854100 z^(3/2) - 948285 z^2 + 1621620 z^(5/2) + 375375 z^3 - 900900 z^(7/2) + 1426425 z^4 + 1203972 z^(9/2) - 1728111 z^5 - 615384 z^(11/2) + 845152 z^6 + 118272 z^(13/2) - 157696 z^7) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((109200 + 163800 Sqrt[z] - 542100 z - 854100 z^(3/2) + 948285 z^2 + 1621620 z^(5/2) - 375375 z^3 - 900900 z^(7/2) - 1426425 z^4 + 1203972 z^(9/2) + 1728111 z^5 - 615384 z^(11/2) - 845152 z^6 + 118272 z^(13/2) + 157696 z^7) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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type='integer'> 163800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -109200 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> 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-1 </cn> <apply> <times /> <cn type='integer'> 1426425 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 900900 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 375375 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1621620 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 948285 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 854100 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02