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variants of this functions
HermiteH






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HermiteH[nu,z] > Series representations > Asymptotic series expansions





http://functions.wolfram.com/07.01.06.0029.01









  


  










Input Form





HermiteH[\[Nu], z] \[Proportional] Piecewise[{{2^\[Nu] z^\[Nu] (1 + O[1/z^2]), Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/2] || (Element[\[Nu], Integers] && \[Nu] >= 0)}, {2^\[Nu] z^\[Nu] (1 + O[1/z^2]) - ((E^(z^2 + I Pi \[Nu]) Sqrt[Pi] z^(-1 - \[Nu]))/Gamma[-\[Nu]]) (1 + O[1/z^2]), Arg[z] > Pi/2}}, 2^\[Nu] z^\[Nu] (1 + O[1/z^2]) - ((E^(z^2 - I Pi \[Nu]) Sqrt[Pi] z^(-1 - \[Nu]))/Gamma[-\[Nu]]) (1 + O[1/z^2])] /; (Abs[z] -> Infinity)










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)





2007-05-02