Carl McBride: Added applications section.

2008-07-07T09:58:44Z

Added applications section.

← Older revision		Revision as of 11:58, 7 July 2008
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	:<math>J_n (z) = \frac{1}{2 \pi i} \oint e^{(z/2)(t-1/t)}t^{-n-1}{\rm d}t</math>		:<math>J_n (z) = \frac{1}{2 \pi i} \oint e^{(z/2)(t-1/t)}t^{-n-1}{\rm d}t</math>
			==Applications in statistical mechanics==
			*[[Computational implementation of integral equations]]
	==See also==		==See also==
	*[http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html Bessel Function of the First Kind -- from Wolfram MathWorld]		*[http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html Bessel Function of the First Kind -- from Wolfram MathWorld]
	[[category: mathematics]]		[[category: mathematics]]

Carl McBride: New page: '''Bessel functions''' of the first kind $J_n(x)$ are defined as the solutions to the Bessel differential equation : $x^2 \frac{d^2y}{dx^2} + x\frac{dy}{dx} + (x^2-n^2)y=0...$

2007-05-31T09:26:04Z

New page: '''Bessel functions''' of the first kind <math>J_n(x)</math> are defined as the solutions to the Bessel differential equation :<math>x^2 \frac{d^2y}{dx^2} + x\frac{dy}{dx} + (x^2-n^2)y=0...

New page

'''Bessel functions''' of the first kind <math>J_n(x)</math> are defined as the solutions to the Bessel differential equation

:<math>x^2 \frac{d^2y}{dx^2} + x\frac{dy}{dx} + (x^2-n^2)y=0</math>

which are nonsingular at the origin. They are sometimes also called ''cylinder functions'' or ''cylindrical harmonics''.
The Bessel function <math>J_n(z)</math> can also be defined by the contour integral

:<math>J_n (z) = \frac{1}{2 \pi i} \oint e^{(z/2)(t-1/t)}t^{-n-1}{\rm d}t</math>

==See also==
*[http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html Bessel Function of the First Kind -- from Wolfram MathWorld]
[[category: mathematics]]

Bessel functions - Revision history

Carl McBride: Added applications section.

Carl McBride: New page: '''Bessel functions''' of the first kind J_n(x) are defined as the solutions to the Bessel differential equation :x^2 \frac{d^2y}{dx^2} + x\frac{dy}{dx} + (x^2-n^2)y=0...

Carl McBride: New page: '''Bessel functions''' of the first kind $J_n(x)$ are defined as the solutions to the Bessel differential equation : $x^2 \frac{d^2y}{dx^2} + x\frac{dy}{dx} + (x^2-n^2)y=0...$