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variants of this functions
HermiteH




Mathematica Notation

Traditional Notation









Polynomials > HermiteH[n,z] > Summation > Infinite summation





http://functions.wolfram.com/05.01.23.0017.01









  


  








Input Form





Sum[(Pochhammer[c, Floor[k/2]]/(Floor[k/2]! Pochhammer[1/2, Floor[k/2]])) HermiteH[k, z] w^k, {k, 0, Infinity}] == Hypergeometric1F1[c, 1/2, (4 z^2 w^2)/(1 + 4 w^2)]/(1 + 4 w^2)^c + ((32 c w^3 z^3)/(3 (1 + 4 w^2)^(c + 2))) Hypergeometric1F1[c + 1, 5/2, (4 z^2 w^2)/(1 + 4 w^2)] + ((2 z t (1 + 4 w^2 - 8 c w^2))/ (1 + 4 w^2)^(c + 1)) Hypergeometric1F1[c, 3/2, (4 z^2 w^2)/(1 + 4 w^2)]








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)





2002-12-18