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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=-23/4, b>=a > For fixed z and a=-23/4, b=17/4





http://functions.wolfram.com/07.23.03.9961.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 17/4, -(11/2), z] == (1/(411840 Pi^(3/2))) (((1/(-1 + z)^4) (4 Sqrt[z] (102960 + 84240 z + 96213 z^2 + 140400 z^3 + 270153 z^4 + 781170 z^5 - 74327040 z^6 + 189984768 z^7 - 167772160 z^8 + 50331648 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^4) (4 Sqrt[z] (102960 + 84240 z + 96213 z^2 + 140400 z^3 + 270153 z^4 + 781170 z^5 - 74327040 z^6 + 189984768 z^7 - 167772160 z^8 + 50331648 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^3)) ((411840 - 617760 Sqrt[z] + 645840 z - 814320 z^(3/2) + 900120 z^2 - 1092546 z^(5/2) + 1304433 z^3 - 1585233 z^(7/2) + 2167659 z^4 - 2707965 z^(9/2) + 4914780 z^5 - 6477120 z^(11/2) + 27156480 z^6 + 121497600 z^(13/2) - 196730880 z^7 - 183238656 z^(15/2) + 260046848 z^8 + 75497472 z^(17/2) - 100663296 z^9) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^4)) ((-411840 - 617760 Sqrt[z] - 645840 z - 814320 z^(3/2) - 900120 z^2 - 1092546 z^(5/2) - 1304433 z^3 - 1585233 z^(7/2) - 2167659 z^4 - 2707965 z^(9/2) - 4914780 z^5 - 6477120 z^(11/2) - 27156480 z^6 + 121497600 z^(13/2) + 196730880 z^7 - 183238656 z^(15/2) - 260046848 z^8 + 75497472 z^(17/2) + 100663296 z^9) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)








Standard Form





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MathML Form







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





2007-05-02