With a success equalled only by Leonhard Euler, Daniel Bernoulli gained or shared no less than ten prizes of the Academy of Sciences of Paris.
Although Bessel was the first to systematically treat of these functions, it is to be noted that in 1732 Daniel Bernoulli obtained the function of zero order as a solution to the problem of the oscillations of a chain suspended at one end.
In 1740 Maclaurin divided with Leonhard Euler and Daniel Bernoulli the prize offered by the French Academy of Sciences for an essay on tides.
The theory of Daniel Bernoulli was opposed also by Jean le Rond d'Alembert.
In 1730 he became professor of physics, and in 1733 he succeeded Daniel Bernoulli in the chair of mathematics.
In 1738 Daniel Bernoulli (1700-1782) published his Hydrodynamica seu de viribus et motibus fluidorum commentarii.
The Academy of Sciences at Paris in 1738 adjudged the prize to his memoir on the nature and properties of fire, and in 1740 his treatise on the tides shared the prize with those of Colin Maclaurin and Daniel Bernoulli - a higher honour than if he had carried it away from inferior rivals.