Difference between revisions of "Graf's Addition Theorem"
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This theorem form the basis for [[Kagemoto and Yue Interaction Theory]]. <math>K_\nu</math> and <math>H_\nu^{(1)}</math> are | This theorem form the basis for [[Kagemoto and Yue Interaction Theory]]. <math>K_\nu</math> and <math>H_\nu^{(1)}</math> are | ||
− | [http://en.wikipedia.org/wiki/Bessel_function | + | [http://en.wikipedia.org/wiki/Bessel_function Bessel functions]. |
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[[Category:Numerical Methods]] | [[Category:Numerical Methods]] | ||
[[Category:Linear Water-Wave Theory]] | [[Category:Linear Water-Wave Theory]] |
Revision as of 12:56, 5 March 2007
Graf's addition theorem for Bessel functions, given in Abramowitz and Stegun 1964, is
which is valid provided that [math]\displaystyle{ r_l \lt R_{jl} }[/math]. Here, [math]\displaystyle{ (R_{jl},\varphi_{jl}) }[/math] are the polar coordinates of the mean centre position of [math]\displaystyle{ \Delta_{l} }[/math] in the local coordinates of [math]\displaystyle{ \Delta_{j} }[/math].
This theorem form the basis for Kagemoto and Yue Interaction Theory. [math]\displaystyle{ K_\nu }[/math] and [math]\displaystyle{ H_\nu^{(1)} }[/math] are Bessel functions.