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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=-19/4, b>=a > For fixed z and a=-19/4, b=-19/4





http://functions.wolfram.com/07.23.03.a90f.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(19/4), 7/2, z] == (1/(323467837875 Pi^(3/2) z^(5/2))) (8 (-2 (11007612 - 384349119 z + 15019886574 z^2 + 258505264535 z^3 + 731138839120 z^4 + 569994295359 z^5 + 121764017062 z^6 + 4758088073 z^7) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (11007612 - 384349119 z + 15019886574 z^2 + 258505264535 z^3 + 731138839120 z^4 + 569994295359 z^5 + 121764017062 z^6 + 4758088073 z^7) EllipticE[(1/2) (1 + Sqrt[z])] + (11007612 + 5503806 Sqrt[z] - 384349119 z - 191715909 z^(3/2) + 15019886574 z^2 + 47927637800 z^(5/2) + 258505264535 z^3 + 385467956425 z^(7/2) + 731138839120 z^4 + 749334272310 z^(9/2) + 569994295359 z^5 + 442707561997 z^(11/2) + 121764017062 z^6 + 73446150212 z^(13/2) + 4758088073 z^7 + 2109682575 z^(15/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (-11007612 + 5503806 Sqrt[z] + 384349119 z - 191715909 z^(3/2) - 15019886574 z^2 + 47927637800 z^(5/2) - 258505264535 z^3 + 385467956425 z^(7/2) - 731138839120 z^4 + 749334272310 z^(9/2) - 569994295359 z^5 + 442707561997 z^(11/2) - 121764017062 z^6 + 73446150212 z^(13/2) - 4758088073 z^7 + 2109682575 z^(15/2)) 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'> 5503806 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 11007612 </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> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2109682575 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4758088073 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 73446150212 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> 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Date Added to functions.wolfram.com (modification date)





2007-05-02