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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=-23/4, b>=a > For fixed z and a=-23/4, b=-7/4





http://functions.wolfram.com/07.23.03.9299.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(7/4), 9/2, z] == (1/(389117468025 Pi^(3/2) z^(7/2))) (16 (8 (1009470 - 19482771 z + 226794260 z^2 - 3572615277 z^3 - 22708645542 z^4 - 17599917005 z^5 - 687573432 z^6 + 75949965 z^7 - 7815444 z^8 + 445536 z^9) EllipticE[(1/2) (1 - Sqrt[z])] - 8 (1009470 - 19482771 z + 226794260 z^2 - 3572615277 z^3 - 22708645542 z^4 - 17599917005 z^5 - 687573432 z^6 + 75949965 z^7 - 7815444 z^8 + 445536 z^9) EllipticE[(1/2) (1 + Sqrt[z])] - (4037880 + 2018940 Sqrt[z] - 77931084 z - 38797297 z^(3/2) + 907177040 z^2 + 450425514 z^(5/2) - 14290461108 z^3 - 31428842247 z^(7/2) - 90834582168 z^4 - 97336729160 z^(9/2) - 70399668020 z^5 - 48882051855 z^(11/2) - 2750293728 z^6 + 73819746 z^(13/2) + 303799860 z^7 - 7690137 z^(15/2) - 31261776 z^8 + 445536 z^(17/2) + 1782144 z^9) EllipticK[(1/2) (1 - Sqrt[z])] + (4037880 - 2018940 Sqrt[z] - 77931084 z + 38797297 z^(3/2) + 907177040 z^2 - 450425514 z^(5/2) - 14290461108 z^3 + 31428842247 z^(7/2) - 90834582168 z^4 + 97336729160 z^(9/2) - 70399668020 z^5 + 48882051855 z^(11/2) - 2750293728 z^6 - 73819746 z^(13/2) + 303799860 z^7 + 7690137 z^(15/2) - 31261776 z^8 - 445536 z^(17/2) + 1782144 z^9) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^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