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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.23.20.0041.02









  


  










Input Form





D[(1 - z^2)^(a + b - 1/2) Hypergeometric2F1[a, b, 1/2, z^2], {z, n}] == 2^(2 n - 2 Floor[n/2]) Pochhammer[1/2 - a, n - Floor[n/2]] Pochhammer[1/2 - b, n - Floor[n/2]] z^(n - 2 Floor[n/2]) (1 - z^2)^(a + b - n - 1/2) Hypergeometric2F1[a - Floor[n/2], b - Floor[n/2], 1/2 + n - 2 Floor[n/2], z^2] /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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Rule Form





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





2001-10-29