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ParabolicCylinderD




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ParabolicCylinderD[nu,z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.41.20.0016.01









  


  








Input Form





D[ParabolicCylinderD[\[Nu], z], {z, n}] == (2^(\[Nu]/2 - n) Sqrt[Pi] n! ((1/(z^n Gamma[(1 - \[Nu])/2])) Sum[(((-1)^k k! z^(2 k))/((n - k)! (2 k - n)!)) Sum[(((-1)^j 2^j Pochhammer[-(\[Nu]/2), j])/(j! (k - j)! Pochhammer[1/2, j])) Hypergeometric1F1[-(\[Nu]/2) + j, 1/2 + j, z^2/2], {j, 0, k}], {k, 0, n}] - (Sqrt[2]/Gamma[-(\[Nu]/2)]) (z^(1 + n) Sum[(((-1)^(-j + n) 2^j Pochhammer[(1 - \[Nu])/2, j])/ (j! (n - j)! Pochhammer[3/2, j])) Hypergeometric1F1[ (1 - \[Nu])/2 + j, 3/2 + j, z^2/2], {j, 0, n}] + (n + 1) z^(1 - n) Sum[(z^(2 k)/((2 k - n + 1)! (n - k)!)) Sum[(((-1)^(-j + k) 2^j Binomial[k, j] Pochhammer[(1 - \[Nu])/2, j])/Pochhammer[3/2, j]) Hypergeometric1F1[(1 - \[Nu])/2 + j, 3/2 + j, z^2/2], {j, 0, k}], {k, 0, n - 1}])))/E^(z^2/4) /; 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)





2007-05-02