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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=-35/8, b>=a > For fixed z and a=-35/8, b=-1/8





http://functions.wolfram.com/07.23.03.bco2.01









  


  










Input Form





Hypergeometric2F1[-(35/8), -(1/8), 6, z] == (1/(29834332625876625 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-13074432 + 156433536 z - 897119181 z^2 + 3433659537 z^3 - 11615269050 z^4 - 143561975430 z^5 - 1967564785 z^6 + 423500685 z^7 - 67999320 z^8 + 5436600 z^9) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (408576 - 4591692 z + 24727626 z^2 - 89645325 z^3 - 9184640850 z^4 - 463595610 z^5 + 101071970 z^6 - 16592085 z^7 + 1359150 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1634304 - 19286064 z + 109057473 z^2 - 412236825 z^3 + 24151043070 z^4 + 7781886510 z^5 - 961689235 z^6 + 197693595 z^7 - 29483100 z^8 + 2174640 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-13074432 + 156433536 z - 897119181 z^2 + 3433659537 z^3 - 11615269050 z^4 - 143561975430 z^5 - 1967564785 z^6 + 423500685 z^7 - 67999320 z^8 + 5436600 z^9) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + 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