Integral representation of n factorial (Euler, 1729)
“Read Euler, read Euler, he is the master of us all.” – Laplace
This is THE best talk about Euler's life and work you'll ever experience
Euler used this integral to define n! for any n>0 (not just integers). This is now known as the Gamma function Γ (evaluated at n+1).
300 years ago Euler enrolled at the University of Basel. He just turned 13.
Bohr*-Mollerup theorem. The Gamma function Γ(n) is the only function defined for n>0 with Γ(1)=1, Γ(n+1) = n Γ(n) and ln(Γ) convex.
*Harald Bohr, Danish mathematician, football player (🥈 1908 Olympics) and brother of Niels Bohr.
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