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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LaguerreL[nu,lambda,z] > Differentiation > Low-order differentiation > With respect to lambda





http://functions.wolfram.com/07.03.20.0004.01









  


  








Input Form





D[LaguerreL[\[Nu], \[Lambda], z], \[Lambda]] == (PolyGamma[1 + \[Lambda] + \[Nu]] - PolyGamma[1 + \[Lambda]]) LaguerreL[\[Nu], \[Lambda], z] + ((z Gamma[1 + \[Lambda] + \[Nu]])/((1 + \[Lambda]) Gamma[2 + \[Lambda]] Gamma[\[Nu]])) HypergeometricPFQ[{{1 - \[Nu]}, {1}, {1, 1 + \[Lambda]}}, {{2, 2 + \[Lambda]}, {}, {2 + \[Lambda]}}, z, z]








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