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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/07.01.06.0007.02









  


  








Input Form





HermiteH[\[Nu], z] \[Proportional] (z^2)^(-\[Nu]/2 - 1) ((Sqrt[Pi]/(2 Gamma[-\[Nu]])) E^z^2 (Sqrt[z^2] - z) (1 + O[1/z^2]) - 2^\[Nu] Sqrt[-z^2] (-z^4)^(\[Nu]/2) (Sqrt[-z^2] Cos[(\[Nu] Pi)/2] + z Sin[(\[Nu] Pi)/2]) (1 + O[1/z^2])) /; (Abs[z] -> Infinity)








Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mn> 2 </mn> <mi> &#957; </mi> </msup> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> &#957; </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> &#957; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> z </mi> <mo> &#8290; 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Rule Form





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





2001-10-29