# Why did Laplace invent the Laplace transform?

Why did Laplace invent the Laplace transform? What was the context? Was it before Fourier or after?

• Easy-to-find and relevant source can be found here, although the information given there seems extremely similar to the Wikipedia history section. Regrettably paywalled but seemingly very useful is this paper. – Danu May 10 '15 at 8:03

Laplace "invented" Laplace transform for applications to probability, namely to prove the special case of what is known now as the central Limit theorem (1785). According to Wikipedia, he used a special case that is called the $z$-transform nowadays (another, more common name is generating function). He also used other forms of the same idea, for example what is called Mellin's transform today.