# Chaitanya's Random Pages

## July 9, 2010

### My Six Favourite Formulas

Filed under: mathematics — ckrao @ 10:38 am

At a later date I will explain them in further detail, but for now here they are!

• $\displaystyle e^{i\pi} + 1 = 0$
• $\displaystyle \int_M d\omega = \int_{\partial M}\omega$
• $\displaystyle \left[e^{{\mathbf a}.\nabla}\right]f({\mathbf x}) = f(\mathbf{ x+a})$
• $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^2} = \frac{\pi^2}{6}$
• $\displaystyle \int_{-\infty}^{\infty} e^{-x^2}\ dx = \sqrt{\pi}$
• $\displaystyle \left(\sum_{n=1}^N n \right)^2 = \sum_{n=1}^N n^3$

1. […] Six Favourite Formulas – #1 August 4, 2010 — ckrao Going back to my earlier post listing my favourite formulas, it’s time to explore the beauty in them. First of all […]

Pingback by My Six Favourite Formulas – #1 « Chaitanya's Random Pages — August 4, 2010 @ 2:28 pm

2. […] Six Favourite Formulas – #3 September 14, 2010 — ckrao Continuing the look at my favourite formulas, behold the […]

Pingback by My Six Favourite Formulas – #3 « Chaitanya's Random Pages — September 14, 2010 @ 1:01 pm

3. […] Favourite Formulas – #4 September 27, 2010 — ckrao Here I will discuss another of my favourite […]

Pingback by My Six Favourite Formulas – #4 « Chaitanya's Random Pages — September 27, 2010 @ 2:07 pm

4. […] to my favourite formulas, we look now at the one I would use more frequently than the others, the Gaussian […]

Pingback by My Six Favourite Formulas – #5 « Chaitanya's Random Pages — October 14, 2010 @ 10:08 am

5. […] is the most elementary of my favourite formulas. I think I first saw this as a Year 8 student and have been enthralled by it ever […]

Pingback by My Six Favourite Formulas – #6 « Chaitanya's Random Pages — October 24, 2010 @ 11:07 am

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