written ei x = cos ( x ) + i sin ( x ) {\displaystyle e^{ix}=\cos(x)+i\sin(x)} . Setting x {\displaystyle x} to a value of π {\displaystyle \pi } , as
I, the copyright holder of this work, hereby publish it under the following license: This image is a derivative work of the following images: File:Pi-symbol
File:Pi eq C over d.svg has 7 embedded translations. en (English) as (Assamese) cs (Czech) ro (Romanian) zh (Chinese) zh-hans (Simplified Chinese) is (Icelandic)
"Record_pi_approximations" # set output "Record_pi_approximations.svg" set terminal win enhanced set key off set title "Record approximations of pi" set
}dx={\frac {i}{2\pi \xi }}(e^{-\pii\xi }-e^{\pii\xi })={\frac {\sin \pi \xi }{\pi \xi }}.} g ^ ( ξ ) = ∫ 0 1 e − 2 π i x ξ d x = i 2 π ξ ( e − 2 π i ξ − 1