- #1

- 293

- 39

- Homework Statement
- try to solve the Gaussian using power series ?

- Relevant Equations
- ∫e^-(x^2)dx

hi guys

i am trying to solve the Gaussian integral using the power series , and i am suck at some point : the idea was to use the following series :

$$\lim_{x→∞}\sum_{n=0}^∞ \frac{(-1)^{n}}{2n+1}\;x^{2n+1} = \frac{\pi}{2}$$

to evaluate the Gaussian integral as its series some how slimier :

$$\int_{0}^{∞} e^{-x^{2}}dx = \lim_{x→∞}\sum_{n=0}^∞ \frac{(-1)^{n}}{(2n+1)n!}\;x^{2n+1} $$

so i want to evalue the series of the gaussian in terms of the other series or any other way to get ##\frac{\pi^{0.5}}{2}## , is it possible ?

i am trying to solve the Gaussian integral using the power series , and i am suck at some point : the idea was to use the following series :

$$\lim_{x→∞}\sum_{n=0}^∞ \frac{(-1)^{n}}{2n+1}\;x^{2n+1} = \frac{\pi}{2}$$

to evaluate the Gaussian integral as its series some how slimier :

$$\int_{0}^{∞} e^{-x^{2}}dx = \lim_{x→∞}\sum_{n=0}^∞ \frac{(-1)^{n}}{(2n+1)n!}\;x^{2n+1} $$

so i want to evalue the series of the gaussian in terms of the other series or any other way to get ##\frac{\pi^{0.5}}{2}## , is it possible ?