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WhittakerM






Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerM[nu,mu,z] > Specific values > Specialized values > For fixed z and half-integer parameters > For fixed z and nu=k/4+-n, mu=-1/4





http://functions.wolfram.com/07.44.03.0067.01









  


  










Input Form





WhittakerM[3/4 + n, -(1/4), z] == ((Sqrt[Pi] Erfi[Sqrt[z]])/(E^(z/2) (2 z^(1/4)))) (LaguerreL[n, -(1/2), z] + 2 (n + 1) LaguerreL[n + 1, -(3/2), z]) + (1/2) E^(z/2) z^(1/4) (Sum[(1/(1 + p)) LaguerreL[n - p - 1, 1/2 + p, z] LaguerreL[p, -(1/2) - p, -z], {p, 0, n - 1}] + 2 (n + 1) Sum[(1/(1 + p)) LaguerreL[n - p, -(1/2) + p, z] LaguerreL[p, -(1/2) - p, -z], {p, 0, n}]) /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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</ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





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