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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=1/4





http://functions.wolfram.com/07.23.03.a9cy.01









  


  










Input Form





Hypergeometric2F1[-(19/4), 1/4, 4, z] == (1/(140821065 Pi z^3)) (256 (2 Sqrt[1 - z] (3040 - 30685 z + 174420 z^2 + 345682 z^3 - 172204 z^4 + 69795 z^5 - 17696 z^6 + 2048 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] - (3040 - 32965 z + 197220 z^2 - 883238 z^3 - 47428 z^4 + 18627 z^5 - 4568 z^6 + 512 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (3040 - 30685 z + 174420 z^2 + 345682 z^3 - 172204 z^4 + 69795 z^5 - 17696 z^6 + 2048 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])]))










Standard Form





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MathML Form







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Rule Form





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





2007-05-02