Kibble–Slepian formula

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In mathematics, the Kibble–Slepian formula, introduced by W.F. Kibble (1945) and D. Slepian (1972), expresses the exponential of a quadratic form in terms of Hermite polynomials, generalizing Mehler's formula to several variables.


  • Kibble, W. F. (1945), "An extension of a theorem of Mehler's on Hermite polynomials", Proc. Cambridge Philos. Soc. 41: 12–15, doi:10.1017/S0305004100022313, MR 0012728 
  • Slepian, David (1972), "On the symmetrized Kronecker power of a matrix and extensions of Mehler's formula for Hermite polynomials", SIAM Journal on Mathematical Analysis 3: 606–616, doi:10.1137/0503060, ISSN 0036-1410, MR 0315173