I am curious about series containing factorials.

Question

Does anyone know any well known series containing factorials that do not have their origins in either Europe nor Asia or have a shared origin and is related to Pi.

Answer 1

$$\pi=\sum_{n=0}^{\infty}{(25n-3)n!(2n)!\over2^{n-1}(3n)!}$$ is due to the American mathematician, Bill Gosper.

$${1\over\pi}={12\over\sqrt{640320^3}}\sum_{k=0}^{\infty}(-1)^k{(6k)!\over(k!)^3(3k)!}{13591409+545140134k\over(640320^3)^k}$$ is due to the American mathematicians (born in Kiev) D. and G. Chudnovsky.