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[parent] Bessel's equation (Definition)
BesselsEquation

"Bessel's equation" is owned by pahio.
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See Also: Laplace equation in cylindrical coordinates, Cauchy residue theorem, properties of entire functions, Frobenius method, table of Laplace transforms

Other names:  Bessel's differential equation, Bessel equation
Also defines:  Bessel's function, Bessel function

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Cross-references: sine, cosine, addition formula, residue, origin, paths, coefficients of Laurent series, point, Laurent expansion, analytic, essential singularity, function, generating function, linearly dependent, gamma function, expressions, similar, ratio, linearly independent, converge, power series, positive, particular solution, integer, solution, roots, indicial equation, equations, vanish, powers, coefficients, derivatives, indefinite, parameter, series, general solution, real, linear differential equation
There are 13 references to this entry.

This is version 19 of Bessel's equation, born on 2007-01-16, modified 2008-02-21.
Object id is 8774, canonical name is BesselsEquation.
Accessed 14545 times total.

Classification:
AMS MSC: 33C10 (Special functions :: Hypergeometric functions :: Bessel and Airy functions, cylinder functions, $_0F_1$)
 34A05 (Ordinary differential equations :: General theory :: Explicit solutions and reductions)
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Rendering problem in HTML mode by pahio on 2007-02-14 02:50:05
Hi, experts of TeX! Rendering the entry "Bessel's equation" does not succeed in HTML mode; it forms great black blocks and the formulas after them are in a mess. I have tried to alter the preamble, but not succeeded. I think the below portion of the code causes the problem, but I cannot fix the thing =o( Please help!

\begin{align}
\begin{cases}
[r^2-p^2]a_0 = 0,\\
[(r+1)^2-p^2]a_1 = 0,\\
[(r+2)^2-p^2]a_2+a_0 = 0,\\
\qquad \qquad \ldots\\
[(r+k)^2-p^2]a_k+a_{k-2} = 0.
\end{cases}
\end{align}

Jussi
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