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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=-25/8





http://functions.wolfram.com/07.23.03.b6b6.01









  


  










Input Form





Hypergeometric2F1[-(45/8), -(25/8), 4, z] == (2048 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-758825600 + 19984383575 z - 390095641650 z^2 - 39673660980891 z^3 - 147807132327120 z^4 - 125475863959215 z^5 - 23427239875130 z^6 - 8781590125 z^7 + 273711900 z^8) EllipticE[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-758825600 + 19984383575 z - 390095641650 z^2 - 39673660980891 z^3 - 147807132327120 z^4 - 125475863959215 z^5 - 23427239875130 z^6 - 8781590125 z^7 + 273711900 z^8) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-758825600 + 19984383575 z - 390095641650 z^2 - 39673660980891 z^3 - 147807132327120 z^4 - 125475863959215 z^5 - 23427239875130 z^6 - 8781590125 z^7 + 273711900 z^8) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-758825600 + 20268943175 z - 397511976225 z^2 - 10989021772341 z^3 - 16833867884589 z^4 + 13189278971925 z^5 + 13789717003405 z^6 + 1256451667625 z^7 - 35650974975 z^8 + 1094847600 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (29225329855196475 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^3)










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