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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=-41/8, b>=a > For fixed z and a=-41/8, b=35/8





http://functions.wolfram.com/07.23.03.b9fr.01









  


  










Input Form





Hypergeometric2F1[-(41/8), 35/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-114196480 + 171740800 z + 113070825 z^2 + 203820225 z^3 + 832479375 z^4 - 40007058741 z^5 + 134469183420 z^6 - 198111513600 z^7 + 153511787520 z^8 - 61575987200 z^9 + 10138419200 z^10) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-114196480 + 214564480 z + 60377625 z^2 + 150029250 z^3 + 739168500 z^4 - 13505672466 z^5 + 40246374051 z^6 - 55494597600 z^7 + 41038583040 z^8 - 15869235200 z^9 + 2534604800 z^10) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-114196480 + 171740800 z + 113070825 z^2 + 203820225 z^3 + 832479375 z^4 - 40007058741 z^5 + 134469183420 z^6 - 198111513600 z^7 + 153511787520 z^8 - 61575987200 z^9 + 10138419200 z^10) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-114196480 + 171740800 z + 113070825 z^2 + 203820225 z^3 + 832479375 z^4 - 40007058741 z^5 + 134469183420 z^6 - 198111513600 z^7 + 153511787520 z^8 - 61575987200 z^9 + 10138419200 z^10) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (7036938400216725 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^5)










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