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Table 2 The normalized Hermite polynomials

From: Uncertainty Analysis and Optimization of Quasi-Zero Stiffness Air Suspension Based on Polynomial Chaos Method

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