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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/07.03.20.0007.01









  


  










Input Form





D[LaguerreL[\[Nu], \[Lambda], z], {\[Lambda], 2}] == (-(2/Pi)) Sin[\[Nu] Pi] Gamma[\[Lambda] + \[Nu] + 1]^3 Sum[(z^k/k!) HypergeometricPFQRegularized[{\[Lambda] + \[Nu] + 1, \[Lambda] + \[Nu] + 1, \[Lambda] + \[Nu] + 1, 1 + \[Nu] - k}, {\[Lambda] + \[Nu] + 2, \[Lambda] + \[Nu] + 2, \[Lambda] + \[Nu] + 2}, 1], {k, 0, Infinity}] /; !(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





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