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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=-35/8, b>=a > For fixed z and a=-35/8, b=25/8





http://functions.wolfram.com/07.23.03.bd1c.01









  


  










Input Form





Hypergeometric2F1[-(35/8), 25/8, 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-2808960 - 2216445 z - 5661810 z^2 + 207506351 z^3 - 590161936 z^4 + 696232320 z^5 - 383989760 z^6 + 82001920 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-2808960 - 1163085 z - 4542615 z^2 + 68594501 z^3 - 172774177 z^4 + 190231776 z^5 - 99841280 z^6 + 20500480 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-2808960 - 2216445 z - 5661810 z^2 + 207506351 z^3 - 590161936 z^4 + 696232320 z^5 - 383989760 z^6 + 82001920 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-2808960 - 2216445 z - 5661810 z^2 + 207506351 z^3 - 590161936 z^4 + 696232320 z^5 - 383989760 z^6 + 82001920 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (144809283465 Pi (1 + Sqrt[1 - z])^(1/4) z^3)










Standard Form





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MathML Form







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










Rule Form





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





2007-05-02