Second-order differential equations Bessel functions

In quantum mechanics and other branches of mathematical physics, we repeatedly encounter what are called special functions. These are often solutions of second-order differential equations with variable coefficients. The most famous examples are Bessel functions, which we wiU not need in this book. Our first encounter with special functions are the Hermite polynomials, contained in solutions of the Schrodinger equation. In subsequent chapters we will introduce Legendre and Laguerre functions. Sometime in 2004, theU.S. National Institute of Standards and Tec hnology (NIST) will publish an online Digital Library of Mathematical Functions, http / /dlmf. nist. gov, including graphics and cross-references. 

The function Y0 at) so obtained is called Neumann s Bessel function of llio second kind of zero order. Obviously if we add to Yn f) a function which is a constant multiple of >/0(.t) the resulting function is also a solution of the differential equation... 

---