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variants of this functions
LaguerreL






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.03.20.0013.02









  


  










Input Form





D[LaguerreL[\[Nu], \[Lambda], z], {\[Nu], m}] == (m!/Gamma[-\[Lambda]]) Sum[(z^j/(Gamma[\[Lambda] + j + 1] j!)) Sum[(Gamma[\[Nu] + 1 + \[Lambda]]^(k + 1)/(m - k)!) HypergeometricPFQRegularized[{Subscript[a, 1], Subscript[a, 2], \[Ellipsis], Subscript[a, k + 1], 1 + \[Lambda]}, {1 + Subscript[a, 1], 1 + Subscript[a, 2], \[Ellipsis], 1 + Subscript[a, k + 1]}, 1] Sum[(((-1)^(j + k) \[Nu]^(k - m + p) p!)/(k + p - m)!) StirlingS1[j, p], {p, 0, j}], {k, 0, m}], {j, 0, Infinity}] /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, k + 1] == \[Nu] + 1 + \[Lambda] && Element[k, Integers] && k > 0 && Element[m, Integers] && m >= 0 && !(Element[\[Lambda], Integers] && \[Lambda] >= 0)










Standard Form





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MathML Form







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Rule Form





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2001-10-29





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