GLAT - Mathematica and favourite equations

After my futile attempt to take GLAT, I looked up some of the sequences and found pretty comprehensive solutions on Mathworld. It's one of my favourite resources when working on a statistics / mathematical problem. They like to mention two interesting facts:



  • Minutes after posting of the puzzle on their website (the first 10-digit prime number occurring in consecutive digits of e) Wolfram Research CEO Stephen Wolfram sent the solution as a single line of Mathematica code: Select[FromDigits/@Partition[First[RealDigits[E,10,1000]],10,1],PrimeQ,1]
    {7427466391}

and



  • Sergey Brin, President of Technology at google.com. What they may not know is that before cofounding the precursor to Google in 1998 and subsequently becoming a multibillionaire, Brin was an intern at Wolfram Research (makers of Mathematica, as well as sponsors of MathWorld).

In the response to ones favourite mathematical equation, following were the author's favourites.


1. Archimedes' recurrence formula
2. Euler formula
3. Euler-Mascheroni constant
4. Riemann hypothesis
5. Gaussian integral
6. Ramanujan's prime product formula:
7. Zeta-regularized product
8. Mandelbrot set recursion
9. BBP formula
10. Cauchy integral formula


My favourite is tie between Euler's formula and Mandelbrot's set. What's yours?


Reference:


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