Bessel functions

Publicerat den augusti 30, 2012 av mattelararen

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.
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About mattelararen

Licentiate of Philosophy in atomic Physics Master of Science in Physics
Detta inlägg publicerades i Calculus och märktes , . Bokmärk permalänken.

2 Responses to Bessel functions

  1. Profilbild för zsjctm zsjctm skriver:
    oktober 16, 2012 kl. 8:35 am

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