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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=1/8, b>=a > For fixed z and a=1/8, b=43/8





http://functions.wolfram.com/07.23.03.by4p.01









  


  










Input Form





Hypergeometric2F1[1/8, 43/8, 5, z] == (65536 2^(1/4) ((2 (-3072 - 4064 z - 6441 z^2 - 14508 z^3 + 53040 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])])/ Sqrt[1 - z] + (1/Sqrt[1 - z]) (Sqrt[2 - 2 Sqrt[1 - z]] (-3072 - 4064 z - 6441 z^2 - 14508 z^3 + 53040 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]) - ((-3072 - 4064 z - 6441 z^2 - 14508 z^3 + 53040 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])])/ Sqrt[1 - z] + 2 (1536 + 2608 z + 4401 z^2 + 9360 z^3 + 53040 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (4928737275 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)










Standard Form





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MathML Form







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</apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02