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ZernikeR






Mathematica Notation

Traditional Notation









Polynomials > ZernikeR[n,m,z] > Differentiation > Symbolic differentiation





http://functions.wolfram.com/05.18.20.0005.01









  


  










Input Form





D[ZernikeR[n, m, z], {z, h}] == Piecewise[{{(((-1)^((n - m)/2) Gamma[(2 + m + n)/2])/ (Gamma[(2 - m + n)/2] m!)) Sum[(Binomial[h, k] Pochhammer[m - h + k + 1, h - k] z^(m - h) Sum[(Pochhammer[2 j - k + 1, 2 (k - j)]/(k - j)!) (2 z)^(2 j) ((Pochhammer[(2 + m + n)/2, j] Pochhammer[(m - n)/2, j])/ Pochhammer[1 + m, j]) Hypergeometric2F1[(2 + m + n)/2 + j, (m - n)/2 + j, 1 + m + j, z^2], {j, 0, k}])/2^k, {k, 0, h}], Element[(n - m)/2, Integers]}}, 0] /; Element[h, Integers] && h >= 0 && Element[n, Integers] && n >= 0 && Element[m, Integers] && m >= 0 && m <= n










Standard Form





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MathML Form







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</apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





© 1998- Wolfram Research, Inc.