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# Table 2 The normalized Hermite polynomials

Polynomial Order | Hermite polynomials |
---|---|

0th | \(1\) |

1st | \(\xi\) |

2nd | \(\frac{1}{\sqrt 2 }\left( {\xi^{2} - 1} \right)\) |

3rd | \(\frac{1}{\sqrt 6 }\left( {\xi^{3} - 3\xi } \right)\) |

4th | \(\frac{1}{2\sqrt 6 }(\xi^{4} - 6\xi^{2} + 3)\) |

5th | \(\frac{1}{{2\sqrt {30} }}\left( {\xi^{5} - 10\xi^{3} + 15\xi } \right)\) |