Bessel functions

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Inläggsdatum augusti 30, 2012
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Friedrich Wilhelm Bessel (1784-1846) was an outstanding mathematician and astronomer in the 19 th. century. Professor at the Albertina university in the no longer existing town of Königsberg. He was the first astronomer to use the parallax of a star for distance measurements. He also pinned down the positions of 50 000 stars.

In pure mathematics his major achievement is to have deduced the Besselfunctions which are solutions to the Bessel differential equation.

$x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + (x^2 - \alpha^2)y = 0$

The solutions are given by

$J_n(x) = \frac{1}{\pi} \int_0^\pi \cos (n \tau - x \sin \tau) \,\mathrm{d}\tau.$

This equation is encountered in electromagnetic wave-propagation problems and in quantum mechanics when solving the Schrödinger-equation.

Etiketter Bessel function, parallax measurements

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Licentiate of Philosophy in atomic Physics
Master of Science in Physics

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2 svar på ”Bessel functions”

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