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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=-47/8, b>=a > For fixed z and a=-47/8, b=-27/8





http://functions.wolfram.com/07.23.03.b4rl.01









  


  










Input Form





Hypergeometric2F1[-(47/8), -(27/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-813683539968 + 18260202879360 z - 218976300286185 z^2 + 2050578495050475 z^3 - 21788929352207745 z^4 - 612433636568684329 z^5 - 1395332118307873935 z^6 - 809000850918154815 z^7 - 110632602912968075 z^8 - 156458521033155 z^9 + 3717826242372 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-813683539968 + 18260202879360 z - 218976300286185 z^2 + 2050578495050475 z^3 - 21788929352207745 z^4 - 612433636568684329 z^5 - 1395332118307873935 z^6 - 809000850918154815 z^7 - 110632602912968075 z^8 - 156458521033155 z^9 + 3717826242372 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-813683539968 + 18260202879360 z - 218976300286185 z^2 + 2050578495050475 z^3 - 21788929352207745 z^4 - 612433636568684329 z^5 - 1395332118307873935 z^6 - 809000850918154815 z^7 - 110632602912968075 z^8 - 156458521033155 z^9 + 3717826242372 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-813683539968 + 18565334206848 z - 225740442018585 z^2 + 2130866548070520 z^3 - 22536408358336860 z^4 + 475465700116636376 z^5 + 2320913784801663114 z^6 + 2418832145306648760 z^7 + 670529866637306980 z^8 + 30473782433309160 z^9 - 632959917763833 z^10 + 14871304969488 z^11) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(283096502504615770085115 Pi (1 + Sqrt[1 - z])^(1/4) z^5)










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02