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variants of this functions
HermiteH






Mathematica Notation

Traditional Notation









Polynomials > HermiteH[n,z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/05.01.21.0016.01









  


  










Input Form





Integrate[(t^(\[Alpha] - 1) HermiteH[n, t])/E^(a t^2), {t, 0, Infinity}] == n! Sum[((-1)^k 2^(n - 2 k - 1) a^(k - (n + \[Alpha])/2) Gamma[(1/2) (n + \[Alpha]) - k])/(k! (n - 2 k)!), {k, 0, Floor[n/2]}] /; Re[a] > 0 && Re[\[Alpha]] > 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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