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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 4 and fixed z > For fixed z and a=-19/4, b>=a > For fixed z and a=-19/4, b=-5/4





http://functions.wolfram.com/07.23.03.a99l.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(5/4), 6, -z] == (1/(127442359719675 Pi z^5)) (16384 (1 + z)^(1/4) (2 (-428032 - 6440544 z - 48746115 z^2 - 265344310 z^3 - 1456379925 z^4 + 20723056536 z^5 - 13417398813 z^6 + 64940850 z^7 + 6016725 z^8 + 331500 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (-428032 - 6440544 z - 48746115 z^2 - 265344310 z^3 - 1456379925 z^4 + 20723056536 z^5 - 13417398813 z^6 + 64940850 z^7 + 6016725 z^8 + 331500 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (428032 + 6119520 z + 44206635 z^2 + 232887655 z^3 + 1286635350 z^4 - 6105623706 z^5 + 1770889575 z^6 + 121279275 z^7 + 11536200 z^8 + 663000 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])]))










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