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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=-21/4, b>=a > For fixed z and a=-21/4, b=-17/4





http://functions.wolfram.com/07.23.03.a87i.01









  


  










Input Form





Hypergeometric2F1[-(21/4), -(17/4), 11/2, z] == (8 (2 Sqrt[z] (-450840 + 10820160 z - 145023957 z^2 + 1679164851 z^3 + 622766766615 z^4 + 2362753469055 z^5 + 2329637577505 z^6 + 683219875353 z^7 + 47277756021 z^8 + 113998005 z^9) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (-450840 + 10820160 z - 145023957 z^2 + 1679164851 z^3 + 622766766615 z^4 + 2362753469055 z^5 + 2329637577505 z^6 + 683219875353 z^7 + 47277756021 z^8 + 113998005 z^9) EllipticE[(1/2) (1 + Sqrt[z])] - (901680 - 450840 Sqrt[z] - 22316580 z + 10820160 z^(3/2) + 306176715 z^2 - 145023957 z^(5/2) - 3573481821 z^3 + 1679164851 z^(7/2) + 68499558855 z^4 + 622766766615 z^(9/2) + 1037878596615 z^5 + 2362753469055 z^(11/2) + 2566330267585 z^6 + 2329637577505 z^(13/2) + 1913075238345 z^7 + 683219875353 z^(15/2) + 441449420349 z^8 + 47277756021 z^(17/2) + 23369591025 z^9 + 113998005 z^(19/2)) EllipticK[(1/2) (1 - Sqrt[z])] - (-901680 - 450840 Sqrt[z] + 22316580 z + 10820160 z^(3/2) - 306176715 z^2 - 145023957 z^(5/2) + 3573481821 z^3 + 1679164851 z^(7/2) - 68499558855 z^4 + 622766766615 z^(9/2) - 1037878596615 z^5 + 2362753469055 z^(11/2) - 2566330267585 z^6 + 2329637577505 z^(13/2) - 1913075238345 z^7 + 683219875353 z^(15/2) - 441449420349 z^8 + 47277756021 z^(17/2) - 23369591025 z^9 + 113998005 z^(19/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^2)/ (20984732643105 Pi^(3/2) z^(9/2))










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