Explain the significance of the formula
[tex] \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} e^{-\frac{1}{2}x^2} , dx = \frac{1}{\sqrt{2\pi}} \left( x - \frac{x^3}{3\cdot2^2} + \frac{x^5}{5\cdot2^4} - \frac{x^7}{7\cdot2^6} + \frac{x^9}{9\cdot2^8} - \frac{x^{11}}{11\cdot2^{10}} + \cdots \right) [/tex] in probability theory and statistical mechanics.