```python
from sympy import init_printing; init_printing(use_latex='mathjax')
import sympy as sym
```


```python
r, theta, k  = sym.symbols('r theta k')
r, theta, k
```




$$\left ( r, \quad \theta, \quad k\right )$$




```python
n = sym.Symbol('n', positive = True, integer=True)
n
```




$$n$$




```python
def lamb(n,k):
    return sym.Symbol('lambda_%s%s'%(n,k), positive = True)
```


```python
lamb(0,k)
```




$$\lambda_{0k}$$




```python
f = 1 - r**2; f
```




$$- r^{2} + 1$$




```python
integrand = f * sym.besselj(n, lamb(n,k) * r) * sym.cos(n *theta) * r
integrand
```




$$r \left(- r^{2} + 1\right) \cos{\left (n \theta \right )} J_{n}\left(\lambda_{nk} r\right)$$




```python
ank = sym.Integral(integrand, (r, 0, 1), (theta, 0, 2*sym.pi))
ank
```




$$\int_{0}^{2 \pi}\int_{0}^{1} r \left(- r^{2} + 1\right) \cos{\left (n \theta \right )} J_{n}\left(\lambda_{nk} r\right)\, dr\, d\theta$$




```python
solution = ank.doit()
solution
```




$$0$$




```python
integ = lambda n: f * sym.besselj(n, lamb(n,k) * r) * sym.cos(n*theta) * r
```


```python
integ(0)
```




$$r \left(- r^{2} + 1\right) J_{0}\left(\lambda_{0k} r\right)$$




```python
a0k = sym.Integral(integ(0), (r, 0, 1), (theta, 0, 2*sym.pi))
a0k
```




$$\int_{0}^{2 \pi}\int_{0}^{1} r \left(- r^{2} + 1\right) J_{0}\left(\lambda_{0k} r\right)\, dr\, d\theta$$




```python
a0k.doit()
```




$$2 \pi \left(- \frac{2 J_{0}\left(\lambda_{0k}\right)}{\lambda_{0k}^{2}} + \frac{4 J_{1}\left(\lambda_{0k}\right)}{\lambda_{0k}^{3}}\right)$$




```python

```

6b7cfeb690c7c180c0242706b0301d4f27edff94
ipynb
Jupyter Notebook
Modulo1/.ipynb_checkpoints/Bessel_Integration-checkpoint.ipynb
esjimenezro/SimRC2018-1
26d1e6c611f3887550cdaf32af65ae689cc8cd81
MIT
Modulo1/.ipynb_checkpoints/Bessel_Integration-checkpoint.ipynb
esjimenezro/SimRC2018-1
26d1e6c611f3887550cdaf32af65ae689cc8cd81
MIT
Modulo1/.ipynb_checkpoints/Bessel_Integration-checkpoint.ipynb
esjimenezro/SimRC2018-1
26d1e6c611f3887550cdaf32af65ae689cc8cd81
MIT
2018-01-22T16:27:05.000Z
2021-06-10T22:09:13.000Z
Qwen/Qwen-72B
1. YES
2. YES