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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 lambda





http://functions.wolfram.com/07.03.20.0015.02









  


  










Input Form





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