Bessel function

Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are the canonical solutions y(x) of Bessel's differential equation

for an arbitrary complex number α (the order of the Bessel function). The most important cases are for α an integer or half-integer.

Although α and −α produce the same differential equation for real α, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of α. Bessel functions are also known as cylinder functions or the cylindrical harmonics because they appear in the solution toLaplace's equation in cylindrical coordinates.

Sumber : http://en.wikipedia.org/wiki/Bessel_function