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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=-5/4, b>=a > For fixed z and a=-5/4, b=23/4





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









  


  










Input Form





Hypergeometric2F1[-(5/4), 23/4, -(7/2), z] == (1/(1966272 Pi^(3/2))) (((1/(-1 + z)^8) (2 (491568 - 2861628 z + 5695459 z^2 - 1843380 z^3 - 5714478 z^4 + 17170296 z^5 - 20097261 z^6 + 12613248 z^7 - 4208640 z^8 + 589824 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^8) (2 (491568 - 2861628 z + 5695459 z^2 - 1843380 z^3 - 5714478 z^4 + 17170296 z^5 - 20097261 z^6 + 12613248 z^7 - 4208640 z^8 + 589824 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^7)) ((-491568 + 245784 Sqrt[z] + 2615844 z - 1205512 z^(3/2) - 4489947 z^2 + 1751211 z^(5/2) + 92169 z^3 + 645183 z^(7/2) + 5069295 z^4 - 8333655 z^(9/2) - 8836641 z^5 + 13119453 z^(11/2) + 6977808 z^6 - 9857664 z^(13/2) - 2755584 z^7 + 3766272 z^(15/2) + 442368 z^8 - 589824 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^8)) ((491568 + 245784 Sqrt[z] - 2615844 z - 1205512 z^(3/2) + 4489947 z^2 + 1751211 z^(5/2) - 92169 z^3 + 645183 z^(7/2) - 5069295 z^4 - 8333655 z^(9/2) + 8836641 z^5 + 13119453 z^(11/2) - 6977808 z^6 - 9857664 z^(13/2) + 2755584 z^7 + 3766272 z^(15/2) - 442368 z^8 - 589824 z^(17/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










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