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variants of this functions
Hypergeometric2F1Regularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.24.20.0032.02









  


  










Input Form





D[(1 - z^2)^(b + Floor[n/2] - 1/2) Hypergeometric2F1Regularized[ c - 1/2 + Floor[n/2], b, c, z^2], {z, n}] == (-1)^Floor[n/2] 2^(2 Floor[n/2]) Pochhammer[1/2, Floor[n/2]] Pochhammer[1/2 + n - 2 Floor[n/2], Floor[n/2]] Pochhammer[c - b, n - Floor[n/2]] z^(n - 2 Floor[n/2]) (1 - z^2)^(b - n + Floor[n/2] - 1/2) Hypergeometric2F1Regularized[c - 1/2, b, c + n - 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