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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=-13/4, b>=a > For fixed z and a=-13/4, b=23/4





http://functions.wolfram.com/07.23.03.acw0.01









  


  








Input Form





Hypergeometric2F1[-(13/4), 23/4, -(9/2), z] == (1/(35392896 Pi^(3/2))) (((1/(-1 + z)^7) (2 (-8848224 + 24086832 z - 5749590 z^2 - 6655187 z^3 - 15105475 z^4 - 101846745 z^5 + 567477109 z^6 - 982510720 z^7 + 824457216 z^8 - 346357760 z^9 + 58720256 z^10) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^7) (2 (-8848224 + 24086832 z - 5749590 z^2 - 6655187 z^3 - 15105475 z^4 - 101846745 z^5 + 567477109 z^6 - 982510720 z^7 + 824457216 z^8 - 346357760 z^9 + 58720256 z^10) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((8848224 - 4424112 Sqrt[z] - 19662720 z + 7987980 z^(3/2) - 2238390 z^2 + 4293905 z^(5/2) + 2361282 z^3 + 823669 z^(7/2) + 14281806 z^4 - 6570333 z^(9/2) + 108417078 z^5 - 204932869 z^(11/2) - 362544240 z^6 + 561907840 z^(13/2) + 420602880 z^7 - 604600320 z^(15/2) - 219856896 z^8 + 302317568 z^(17/2) + 44040192 z^9 - 58720256 z^(19/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((8848224 + 4424112 Sqrt[z] - 19662720 z - 7987980 z^(3/2) - 2238390 z^2 - 4293905 z^(5/2) + 2361282 z^3 - 823669 z^(7/2) + 14281806 z^4 + 6570333 z^(9/2) + 108417078 z^5 + 204932869 z^(11/2) - 362544240 z^6 - 561907840 z^(13/2) + 420602880 z^7 + 604600320 z^(15/2) - 219856896 z^8 - 302317568 z^(17/2) + 44040192 z^9 + 58720256 z^(19/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)








Standard Form





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MathML Form







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<sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 44040192 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 302317568 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 219856896 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 604600320 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 420602880 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 561907840 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> 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Rule Form





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





2007-05-02