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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 5 and fixed z > For fixed z and a=5, b>=a > For fixed z and a=5, b=6





http://functions.wolfram.com/07.23.03.b4b7.01









  


  








Input Form





Hypergeometric2F1[5, 6, -(24/5), z] == (1/(742187500 (-1 + z)^15)) (-742187500 + 15771484375 z - 173144531250 z^2 + 1380175781250 z^3 - 10087792968750 z^4 + 102255644531250 z^5 + 949401830743674 z^6 + 1296780019266870 z^7 + 468580791631950 z^8 + 38948768557375 z^9 + 164086422500 z^10) + (1/(48828125 (1 - z)^(79/5))) (93270177 Sqrt[2 (5 + Sqrt[5])] z^(29/5) (119119 + 350350 z + 269500 z^2 + 61250 z^3 + 3125 z^4) ArcTan[1 - ((1 - Sqrt[5]) z^(1/5))/ (4 (1 - z)^(1/5)), -((Sqrt[5/8 + Sqrt[5]/8] z^(1/5))/ (1 - z)^(1/5))]) + (1/(48828125 (1 - z)^(79/5))) (93270177 Sqrt[10 - 2 Sqrt[5]] z^(29/5) (119119 + 350350 z + 269500 z^2 + 61250 z^3 + 3125 z^4) ArcTan[1 - ((1 + Sqrt[5]) z^(1/5))/ (4 (1 - z)^(1/5)), -((Sqrt[5/8 - Sqrt[5]/8] z^(1/5))/ (1 - z)^(1/5))]) - (1/(48828125 (1 - z)^(79/5))) (186540354 z^(29/5) (119119 + 350350 z + 269500 z^2 + 61250 z^3 + 3125 z^4) Log[1 + z^(1/5)/(1 - z)^(1/5)]) - (1/(97656250 (1 - z)^(79/5))) (93270177 (-1 + Sqrt[5]) z^(29/5) (119119 + 350350 z + 269500 z^2 + 61250 z^3 + 3125 z^4) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) + (1/(97656250 (1 - z)^(79/5))) (93270177 (1 + Sqrt[5]) z^(29/5) (119119 + 350350 z + 269500 z^2 + 61250 z^3 + 3125 z^4) Log[1 - ((1 + Sqrt[5]) z^(1/5))/ (2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])








Standard Form





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MathML Form







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type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 949401830743674 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 102255644531250 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10087792968750 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1380175781250 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 173144531250 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15771484375 </cn> <ci> z </ci> </apply> <cn type='integer'> -742187500 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02