In mathematics, Bessel functions, first defined by the
mathematician Daniel Bernoulli and generalized by Friedrich Bessel,
are canonical solutions y(x) of Bessel's differential equation:
for an arbitrary real or complex number α (the order of the Bessel
function); the most common and important cases are for α an integer
or half-integer.
Although α and −α produce the same differential equation, it
is conventional to define different Bessel functions for these two
orders, so that the Bessel functions are mostly smooth functions of
α. Bessel functions are also known as cylinder functions or
cylindrical harmonics because they are found in the solution to
Laplace's equation in cylindrical coordinates.
From Wikipedia.
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