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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=9/4





http://functions.wolfram.com/07.23.03.9731.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 9/4, 9/2, z] == (1/(195634725 Pi^(3/2) z^(7/2))) (16 (8 (201894 - 908523 z + 538384 z^2 + 2355430 z^3 - 10899614 z^4 + 19240573 z^5 - 18822416 z^6 + 10776448 z^7 - 3399680 z^8 + 458752 z^9) EllipticE[(1/2) (1 - Sqrt[z])] - 8 (201894 - 908523 z + 538384 z^2 + 2355430 z^3 - 10899614 z^4 + 19240573 z^5 - 18822416 z^6 + 10776448 z^7 - 3399680 z^8 + 458752 z^9) EllipticE[(1/2) (1 + Sqrt[z])] - (807576 + 403788 Sqrt[z] - 3634092 z - 1783397 z^(3/2) + 2153536 z^2 + 942172 z^(5/2) + 9421720 z^3 - 7491374 z^(7/2) - 43598456 z^4 + 15278560 z^(9/2) + 76962292 z^5 - 16263029 z^(11/2) - 75289664 z^6 + 9890176 z^(13/2) + 43105792 z^7 - 3270656 z^(15/2) - 13598720 z^8 + 458752 z^(17/2) + 1835008 z^9) EllipticK[(1/2) (1 - Sqrt[z])] + (807576 - 403788 Sqrt[z] - 3634092 z + 1783397 z^(3/2) + 2153536 z^2 - 942172 z^(5/2) + 9421720 z^3 + 7491374 z^(7/2) - 43598456 z^4 - 15278560 z^(9/2) + 76962292 z^5 + 16263029 z^(11/2) - 75289664 z^6 - 9890176 z^(13/2) + 43105792 z^7 + 3270656 z^(15/2) - 13598720 z^8 - 458752 z^(17/2) + 1835008 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