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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=-11/2, b>=a > For fixed z and a=-11/2, b=23/4





http://functions.wolfram.com/07.23.03.a84t.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 23/4, 6, z] == (8 Sqrt[2] (-2 (393216 + 823296 z + 2264832 z^2 + 8684544 z^3 + 59966592 z^4 - 1522718400 z^5 + 5815494160 z^6 - 9876840880 z^7 + 8744824140 z^8 - 3962492430 z^9 + 729183975 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (393216 + 823296 z + 2264832 z^2 + 8684544 z^3 + 59966592 z^4 - 1522718400 z^5 + 5815494160 z^6 - 9876840880 z^7 + 8744824140 z^8 - 3962492430 z^9 + 729183975 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (393216 + 823296 z + 2264832 z^2 + 8684544 z^3 + 59966592 z^4 - 1522718400 z^5 + 5815494160 z^6 - 9876840880 z^7 + 8744824140 z^8 - 3962492430 z^9 + 729183975 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (393216 + 823296 z + 2264832 z^2 + 8684544 z^3 + 59966592 z^4 - 1522718400 z^5 + 5815494160 z^6 - 9876840880 z^7 + 8744824140 z^8 - 3962492430 z^9 + 729183975 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (393216 + 823296 z + 2264832 z^2 + 8684544 z^3 + 59966592 z^4 - 1522718400 z^5 + 5815494160 z^6 - 9876840880 z^7 + 8744824140 z^8 - 3962492430 z^9 + 729183975 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-393216 - 1019904 z - 2836224 z^2 - 10292736 z^3 - 65654400 z^4 + 36684480 z^5 + 1659840560 z^6 - 5007736240 z^7 + 6041507940 z^8 - 3379145250 z^9 + 729183975 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (5805264465 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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<apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02