What is this equation with zeta from a T-Shirt in a video?

Question

There's an equation on a T-shirt in the music video by Remy Zero for "Gramarye". There's not a completely clear shot of it, but it's something along the lines of:

$$?^{???}(z) = \frac{n !}{2 \pi ?} \int_{C} \frac{f(\zeta)}{(\zeta - z)^{n+1}} d\zeta \,$$

Can anyone fill in the blanks and identify what that is? Searched around a bit on line integrals and zeta functions and didn't find anything

Gramarye T-shirt

It's $f^{(n)}(z)$. See Cauchy's generalized integral formula. Now I really want that shirt. — Cameron Williams, Jul 22 '14 at 03:39
That's not a zeta function. Zeta there is just a dummy variable. — mweiss, Jul 22 '14 at 03:39

score 3 · Accepted Answer · answered Jul 22 '14 at 04:07

3

Turning comment into an answer.

That is Cauchy's integral formula. The full formula is given by

$$f^{(n)}(z) = \frac{n !}{2 \pi i} \int_{C}\! \frac{f(\zeta)}{(\zeta - z)^{n+1}} \mathrm{d}\zeta $$

answered Jul 22 '14 at 04:07

Brad

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Is it so worthy to be on a t-shirt? – MonK Jul 22 '14 at 04:37
@Sid It doesn't take much to make it onto a shirt in the first place... so I'd imagine it's as good as anything. :-) – HostileFork says dont trust SE Jul 22 '14 at 07:10

What is this equation with zeta from a T-Shirt in a video?

1 Answers1