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variants of this functions
HermiteH






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HermiteH[nu,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > General case





http://functions.wolfram.com/07.01.06.0016.01









  


  










Input Form





HermiteH[\[Nu], z] == Subscript[F, Infinity][z, \[Nu]] /; Subscript[F, m][z, \[Nu]] == 2^\[Nu] Sqrt[Pi] ((1/Gamma[(1 - \[Nu])/2]) Sum[(Pochhammer[-(\[Nu]/2), k] z^(2 k))/ (Pochhammer[1/2, k] k!), {k, 0, m}] - ((2 z)/Gamma[-(\[Nu]/2)]) Sum[(Pochhammer[(1 - \[Nu])/2, k] z^(2 k))/(Pochhammer[3/2, k] k!), {k, 0, m}]) == HermiteH[\[Nu], z] - ((2^\[Nu] Sqrt[Pi] z^(2 + 2 m))/(1 + m)!) ((Pochhammer[-(\[Nu]/2), 1 + m]/(Gamma[(1 - \[Nu])/2] Pochhammer[1/2, 1 + m])) HypergeometricPFQ[{1, 1 + m - \[Nu]/2}, {3/2 + m, 2 + m}, z^2] - ((2 Pochhammer[(1 - \[Nu])/2, 1 + m] z)/ (Gamma[-(\[Nu]/2)] Pochhammer[3/2, 1 + m])) HypergeometricPFQ[ {1, 3/2 + m - \[Nu]/2}, {2 + m, 5/2 + m}, z^2]) && Element[m, Integers] && m >= 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)





2007-05-02





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