Bessel function

In mathematics, Bessel functions, first defined by the Swiss mathematician Daniel Bernoulli and named after Friedrich Bessel, are canonical solutions y(x) of Bessel's differential equation:

Related Topics:
Mathematics - Swiss - Mathematician - Daniel Bernoulli - Friedrich Bessel - Differential equation

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:x^2 rac{d^2 y}{dx^2} + x rac{dy}{dx} + (x^2 - lpha^2)y = 0

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for an arbitrary real number α (the order). The most common and important special case is where α is an integer, n.

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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).

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