What is this infinite series? may be Laplace transform series, or only an infinite series without name?

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L(t)= \int_{t}^{\infty}\frac{f(t)}{e^{st}} dt =-0 +

\frac{1}{e^{st}}\sum_{n=0}^{\infty}\frac{f^{(n)}(t)}{s^{(n+1)}}

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IL(L(t))= \frac{1}{2\Pi i}\int_{\gamma-i\infty}^{\gamma+i\infty}e^{st}L(t) ds=\frac{1}{2\Pi

i}\oint_{c}e^{st}L(t) ds = \frac{1}{2\Pi i}\sum_{n=0}^{\infty}\oint_{c}\frac{f^{(n)}(t)}{s^{(n+1)}}

ds

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= \frac{1}{2\Pi i}f(t)\oint_{c}\frac{1}{s} ds = \frac{1}{2\Pi i}f(t)\int_{0}^{2\Pi}\frac{is}{s}

d\Theta = f(t)

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