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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=-17/8





http://functions.wolfram.com/07.23.03.b6e3.01









  


  










Input Form





Hypergeometric2F1[-(45/8), -(17/8), 5, z] == (65536 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-728472576 + 14258333024 z - 157102272431 z^2 + 1646707989654 z^3 + 90623927464035 z^4 + 180447723340500 z^5 + 64131105022215 z^6 + 61849765670 z^7 - 4685035355 z^8 + 218969520 z^9) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[1 - z] (-728472576 + 14258333024 z - 157102272431 z^2 + 1646707989654 z^3 + 90623927464035 z^4 + 180447723340500 z^5 + 64131105022215 z^6 + 61849765670 z^7 - 4685035355 z^8 + 218969520 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-728472576 + 14258333024 z - 157102272431 z^2 + 1646707989654 z^3 + 90623927464035 z^4 + 180447723340500 z^5 + 64131105022215 z^6 + 61849765670 z^7 - 4685035355 z^8 + 218969520 z^9) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - 4 (-182118144 + 3632877560 z - 40593612605 z^2 + 426049747110 z^3 + 5336631561639 z^4 + 1165069047450 z^5 - 5774834628255 z^6 - 1175273279950 z^7 + 64071393925 z^8 - 4789958250 z^9 + 218969520 z^10) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (2250350398850128575 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^4)










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