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





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









  


  








Input Form





Hypergeometric2F1[5, 6, -(17/4), z] == (1/88986353664) ((1/(-1 + z)^15) (8 (-11123294208 + 245366784000 z - 2853049466880 z^2 + 25124635934720 z^3 - 227926314319872 z^4 + 6086492996763648 z^5 + 28638448740034595 z^6 + 30384714542604420 z^7 + 9241893307773600 z^8 + 654867747780992 z^9 + 1682771650560 z^10)) + (1/(1 - z)^(61/4)) (336882996450 Sqrt[2] z^(21/4) (59015 + 188848 z + 156288 z^2 + 37888 z^3 + 2048 z^4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (1/(1 - z)^(61/4)) (336882996450 Sqrt[2] z^(21/4) (59015 + 188848 z + 156288 z^2 + 37888 z^3 + 2048 z^4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/(1 - z)^(61/4)) (168441498225 Sqrt[2] z^(21/4) (59015 + 188848 z + 156288 z^2 + 37888 z^3 + 2048 z^4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) + (1/(1 - z)^(61/4)) (168441498225 Sqrt[2] z^(21/4) (59015 + 188848 z + 156288 z^2 + 37888 z^3 + 2048 z^4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))








Standard Form





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MathML Form







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</semantics> </math>










Rule Form





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





2007-05-02