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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=-45/8, b>=a > For fixed z and a=-45/8, b=-1/8





http://functions.wolfram.com/07.23.03.b6kb.01









  


  










Input Form





Hypergeometric2F1[-(45/8), -(1/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (457080832 - 6186660480 z + 40704786135 z^2 - 181959264890 z^3 + 736137900225 z^4 + 10085244964260 z^5 + 96569506825 z^6 - 29309024250 z^7 + 7166536575 z^8 - 1150050000 z^9 + 88323840 z^10) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[1 - z] (457080832 - 6186660480 z + 40704786135 z^2 - 181959264890 z^3 + 736137900225 z^4 + 10085244964260 z^5 + 96569506825 z^6 - 29309024250 z^7 + 7166536575 z^8 - 1150050000 z^9 + 88323840 z^10) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (457080832 - 6186660480 z + 40704786135 z^2 - 181959264890 z^3 + 736137900225 z^4 + 10085244964260 z^5 + 96569506825 z^6 - 29309024250 z^7 + 7166536575 z^8 - 1150050000 z^9 + 88323840 z^10) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - (457080832 - 6358065792 z + 42977915175 z^2 - 196614084290 z^3 + 800519509725 z^4 + 891053148360 z^5 - 1867586167535 z^6 + 439635363750 z^7 - 130501348725 z^8 + 30832840500 z^9 - 4769487360 z^10 + 353295360 z^11) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (2342201435537888925 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^5)










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