Bessel Function

Bessel Function

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 (e.g., 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.

Read more about Bessel Function:  Applications of Bessel Function, Definitions, Asymptotic Forms, Properties, Multiplication Theorem, Bourget's Hypothesis, Selected Identities

Famous quotes containing the word function:

    Advocating the mere tolerance of difference between women is the grossest reformism. It is a total denial of the creative function of difference in our lives. Difference must be not merely tolerated, but seen as a fund of necessary polarities between which our creativity can spark like a dialectic.
    Audre Lorde (1934–1992)