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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 nu





http://functions.wolfram.com/07.03.20.0003.01









  


  










Input Form





D[LaguerreL[\[Nu], \[Lambda], z], {\[Nu], 2}] == (Gamma[1 + \[Nu] + \[Lambda]]/\[Nu]!^2) Sum[((z^k Pochhammer[-\[Nu], k])/(k! Gamma[1 + k + \[Lambda]])) (Gamma[1 + \[Nu]] PolyGamma[k - \[Nu]] PolyGamma[1 + \[Nu]] + \[Nu]! (PolyGamma[k - \[Nu]]^2 - PolyGamma[k - \[Nu]] (Pi Cot[\[Nu] Pi] + PolyGamma[-\[Nu]] + 2 PolyGamma[1 + \[Nu] + \[Lambda]]) + PolyGamma[1, k - \[Nu]])), {k, 0, Infinity}] + (-Pi^2 + 2 Pi Cot[\[Nu] Pi] PolyGamma[1 + \[Nu] + \[Lambda]] + PolyGamma[1 + \[Nu] + \[Lambda]]^2 + PolyGamma[1, 1 + \[Nu] + \[Lambda]]) LaguerreL[\[Nu], \[Lambda], z]










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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