P. 542, last boxed set of equations: Difference between revisions

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The first equation should be
a_{m,n} = \frac{\hat r}{\alpha z_{m,n}} \frac{\int_0^{\hat r} \int_0 ^{2 \pi} r f(r, \theta) \cos m \theta J_m (z_{m,n} r/\hat r) d \theta dr}{\left( \int_0^{2 \pi} \cos^2 m \theta d \theta \right) \left(\int_0^{\hat r} r J^2_m (z_{m,n} r/\hat r) \right)}</math>
The second equation should be
b_{m,n} = \frac{\hat r}{\alpha z_{m,n}} \frac{\int_0^{\hat r} \int_0 ^{2 \pi} r f(r, \theta) \sin m \theta J_m (z_{m,n} r/\hat r) d \theta dr}{\left( \int_0^{2 \pi} \cos^2 m \theta d \theta \right) \left(\int_0^{\hat r} r J^2_m (z_{m,n} r/\hat r) \right)}</math>
The third equation should be
The third equation should be


<math>c_{m,n} = \frac{\hat r}{\alpha z_{m,n}} \frac{\int_0^{\hat r} \int_0 ^{2 \pi} r g(r, \theta) \cos m \theta J_m (z_{m,n} r/\hat r) d \theta dr}{\left( \int_0^{2 \pi} \cos^2 m \theta d \theta \right) \left(\int_0^{\hat r} J^2_m (z_{m,n} r/\hat r) \right)}</math>
<math>c_{m,n} = \frac{\hat r}{\alpha z_{m,n}} \frac{\int_0^{\hat r} \int_0 ^{2 \pi} r g(r, \theta) \cos m \theta J_m (z_{m,n} r/\hat r) d \theta dr}{\left( \int_0^{2 \pi} \cos^2 m \theta d \theta \right) \left(\int_0^{\hat r} r J^2_m (z_{m,n} r/\hat r) \right)}</math>


and the fourth equation should be
and the fourth equation should be


<math>d_{m,n} = \frac{\hat r}{\alpha z_{m,n}} \frac{\int_0^{\hat r} \int_0 ^{2 \pi} r g(r, \theta) \sin m \theta J_m (z_{m,n} r/\hat r) d \theta dr}{\left( \int_0^{2 \pi} \cos^2 m \theta d \theta \right) \left(\int_0^{\hat r} J^2_m (z_{m,n} r/\hat r) \right)}.</math>
<math>d_{m,n} = \frac{\hat r}{\alpha z_{m,n}} \frac{\int_0^{\hat r} \int_0 ^{2 \pi} r g(r, \theta) \sin m \theta J_m (z_{m,n} r/\hat r) d \theta dr}{\left( \int_0^{2 \pi} \cos^2 m \theta d \theta \right) \left(\int_0^{\hat r} r J^2_m (z_{m,n} r/\hat r) \right)}.</math>
 
 


[[Engineering Differential Equations: Theory and Applications, Springer 2010#Errata|Return to errata.]]
[[Engineering Differential Equations: Theory and Applications, Springer 2010#Errata|Return to errata.]]

Revision as of 14:02, 6 November 2023

The first equation should be

a_{m,n} = \frac{\hat r}{\alpha z_{m,n}} \frac{\int_0^{\hat r} \int_0 ^{2 \pi} r f(r, \theta) \cos m \theta J_m (z_{m,n} r/\hat r) d \theta dr}{\left( \int_0^{2 \pi} \cos^2 m \theta d \theta \right) \left(\int_0^{\hat r} r J^2_m (z_{m,n} r/\hat r) \right)}</math>

The second equation should be

b_{m,n} = \frac{\hat r}{\alpha z_{m,n}} \frac{\int_0^{\hat r} \int_0 ^{2 \pi} r f(r, \theta) \sin m \theta J_m (z_{m,n} r/\hat r) d \theta dr}{\left( \int_0^{2 \pi} \cos^2 m \theta d \theta \right) \left(\int_0^{\hat r} r J^2_m (z_{m,n} r/\hat r) \right)}</math>

The third equation should be

cm,n=r^αzm,n0r^02πrg(r,θ)cosmθJm(zm,nr/r^)dθdr(02πcos2mθdθ)(0r^rJm2(zm,nr/r^))

and the fourth equation should be

dm,n=r^αzm,n0r^02πrg(r,θ)sinmθJm(zm,nr/r^)dθdr(02πcos2mθdθ)(0r^rJm2(zm,nr/r^)).


Return to errata.