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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 8 and fixed z and a<0 > For fixed z and a=-39/8, b>=a > For fixed z and a=-39/8, b=45/8





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









  


  










Input Form





Hypergeometric2F1[-(39/8), 45/8, 2, z] == (16 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-28224105 + 3499793924 z - 31362338304 z^2 + 90958095360 z^3 - 104966062080 z^4 + 41912893440 z^5) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-28224105 + 3499793924 z - 31362338304 z^2 + 90958095360 z^3 - 104966062080 z^4 + 41912893440 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-28224105 + 3499793924 z - 31362338304 z^2 + 90958095360 z^3 - 104966062080 z^4 + 41912893440 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-28224105 - 2624836861 z + 51926993712 z^2 - 263946329856 z^3 + 547189800960 z^4 - 500197294080 z^5 + 167651573760 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (49081718595 Pi (1 + Sqrt[1 - z])^(1/4) z)










Standard Form





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MathML Form







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</semantics> </math>










Rule Form





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





2007-05-02