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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=-11/4, b>=a > For fixed z and a=-11/4, b=21/4





http://functions.wolfram.com/07.23.03.ado5.01









  


  








Input Form





Hypergeometric2F1[-(11/4), 21/4, -(9/2), z] == (1/(318240 Pi^(3/2))) (((1/(-1 + z)^7) (2 Sqrt[z] (-159120 + 543660 z - 375921 z^2 - 245973 z^3 - 310947 z^4 + 12142221 z^5 - 26083008 z^6 + 23893504 z^7 - 10518528 z^8 + 1835008 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^7) (2 Sqrt[z] (-159120 + 543660 z - 375921 z^2 - 245973 z^3 - 310947 z^4 + 12142221 z^5 - 26083008 z^6 + 23893504 z^7 - 10518528 z^8 + 1835008 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((-318240 + 477360 Sqrt[z] + 848640 z - 1392300 z^(3/2) - 139230 z^2 + 515151 z^(5/2) - 547638 z^3 + 793611 z^(7/2) - 1011738 z^4 + 1322685 z^(9/2) - 3202290 z^5 - 8939931 z^(11/2) + 14134848 z^6 + 11948160 z^(13/2) - 17251840 z^7 - 6641664 z^(15/2) + 9142272 z^8 + 1376256 z^(17/2) - 1835008 z^9) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((318240 + 477360 Sqrt[z] - 848640 z - 1392300 z^(3/2) + 139230 z^2 + 515151 z^(5/2) + 547638 z^3 + 793611 z^(7/2) + 1011738 z^4 + 1322685 z^(9/2) + 3202290 z^5 - 8939931 z^(11/2) - 14134848 z^6 + 11948160 z^(13/2) + 17251840 z^7 - 6641664 z^(15/2) - 9142272 z^8 + 1376256 z^(17/2) + 1835008 z^9) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)








Standard Form





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MathML Form







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<cn type='integer'> 14134848 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8939931 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3202290 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1322685 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1011738 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 793611 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 547638 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 515151 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 139230 </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'> 1392300 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 848640 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 477360 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 318240 </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> 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Date Added to functions.wolfram.com (modification date)





2007-05-02