10.1: A- Series and Integrals
- Page ID
- 6392
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\[ \frac{1}{1-x}=1+x+x^{2}+x^{3}+x^{4}+\cdots \quad \text { for }|x|<1 \quad \text { (the "geometric series") }\]
\[ e^{x}=1+x+\frac{1}{2 !} x^{2}+\frac{1}{3 !} x^{3}+\frac{1}{4 !} x^{4}+\cdots\]
\[ \ln (1+x)=x-\frac{1}{2} x^{2}+\frac{1}{3} x^{3}-\frac{1}{4} x^{4}+\cdots \quad \text { for }|x|<1\]
\[ \int_{-\infty}^{+\infty} e^{-a x^{2}+b x} d x=\sqrt{\frac{\pi}{a}} e^{b^{2} / 4 a} \quad \text { for } a>0 \quad \text { (the "Gaussian integral") }\]