FTP, identify these functions designated J sub n, which are solutions to the equation x squared times y double prime plus x times y prime plus
Shown by Lord Rayleigh to arise from a cylindrical formulation of LaPlace's equation, forms of these functions had been studied by Daniel Bernoulli and Leonhard Euler, but they were not derived in full until 1817. Commonly combined to form Hankel and Neumann functions, they were used to study the three-body problem and later shown to appear in the mathematical descriptions of the diffraction of light, the motions of fluids, and many other physical phenomena. FTP, identify these functions designated J sub n, which are solutions to the equation x squared times y double prime plus x times y prime plus y times the quantity x squared minus n squared equals 0, named for a German astronomer.
Shown by Lord Rayleigh to arise from a cylindrical formulation of LaPlace's equation, forms of these functions had been studied by Daniel Bernoulli and Leonhard Euler, but they were not derived in full until 1817.
Bessel functions