HaloArray.png

Bessel function: Difference between revisions

From Halopedia, the Halo wiki

m (Bot: Fixing redirects)
mNo edit summary
Line 1: Line 1:
{{Era|FS}}
{{Era|HCW}}
{{Ratings}}
 
'''Bessel functions''', in mathematics, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions ''y''(''x'') of Bessel's differential equation:
'''Bessel functions''', in mathematics, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions ''y''(''x'') of Bessel's differential equation:


Line 11: Line 9:


The [[unidentified Covenant AI|artificial intelligence]] aboard the ''[[Ascendant Justice]]'' attempted to use Bessel functions to communicate with [[Cortana]] <ref>'''[[Halo: First Strike]]''', ''page 67''</ref>. [[Dominique]] had a tattoo of a Bessel function on his left wrist.
The [[unidentified Covenant AI|artificial intelligence]] aboard the ''[[Ascendant Justice]]'' attempted to use Bessel functions to communicate with [[Cortana]] <ref>'''[[Halo: First Strike]]''', ''page 67''</ref>. [[Dominique]] had a tattoo of a Bessel function on his left wrist.
==List of appearances==
*''[[Halo: The Fall of Reach]]'' {{1st}}
*''[[Halo: First Strike]]''


==Sources==
==Sources==
<references/>
<references/>
[[Category:Science]]
[[Category:Science]]

Revision as of 18:16, December 11, 2011

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

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

For an arbitrary real or complex number α. The most common and important special case is where α is an integer n, then α is referred to as the order of the Bessel function.

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.

The artificial intelligence aboard the Ascendant Justice attempted to use Bessel functions to communicate with Cortana [1]. Dominique had a tattoo of a Bessel function on his left wrist.

List of appearances

Sources