```python
from sympy import *
```


```python
s=10
```


```python
x = Symbol("x")
```


```python
legpols = []
```


```python
for k in range(0,s+1):
    legpol = 0
    for j in range(0, k+1):
        legpol += (-1)**(j+k) * binomial(k,j) * binomial(j+k,j) * x**j
    legpols.append(sqrt(2*k+1)*legpol)
```


```python
legpols
```




    [1,
     sqrt(3)*(2*x - 1),
     sqrt(5)*(6*x**2 - 6*x + 1),
     sqrt(7)*(20*x**3 - 30*x**2 + 12*x - 1),
     210*x**4 - 420*x**3 + 270*x**2 - 60*x + 3,
     sqrt(11)*(252*x**5 - 630*x**4 + 560*x**3 - 210*x**2 + 30*x - 1),
     sqrt(13)*(924*x**6 - 2772*x**5 + 3150*x**4 - 1680*x**3 + 420*x**2 - 42*x + 1),
     sqrt(15)*(3432*x**7 - 12012*x**6 + 16632*x**5 - 11550*x**4 + 4200*x**3 - 756*x**2 + 56*x - 1),
     sqrt(17)*(12870*x**8 - 51480*x**7 + 84084*x**6 - 72072*x**5 + 34650*x**4 - 9240*x**3 + 1260*x**2 - 72*x + 1),
     sqrt(19)*(48620*x**9 - 218790*x**8 + 411840*x**7 - 420420*x**6 + 252252*x**5 - 90090*x**4 + 18480*x**3 - 1980*x**2 + 90*x - 1),
     sqrt(21)*(184756*x**10 - 923780*x**9 + 1969110*x**8 - 2333760*x**7 + 1681680*x**6 - 756756*x**5 + 210210*x**4 - 34320*x**3 + 2970*x**2 - 110*x + 1)]




```python

```

2e1cdc2d696a4ad20594a8f52310690f673de824
ipynb
Jupyter Notebook
prototyping/Legendre_Polynomials_Normalised.ipynb
krystophny/GeometricIntegrators.jl
7855e977b014c8ba119f6bb73c6ed9bf96f04b1d
MIT
2020-12-29T10:41:35.000Z
2022-03-21T11:48:39.000Z
prototyping/Legendre_Polynomials_Normalised.ipynb
krystophny/GeometricIntegrators.jl
7855e977b014c8ba119f6bb73c6ed9bf96f04b1d
MIT
2020-11-16T16:45:50.000Z
2022-03-09T17:51:11.000Z
prototyping/Legendre_Polynomials_Normalised.ipynb
krystophny/GeometricIntegrators.jl
7855e977b014c8ba119f6bb73c6ed9bf96f04b1d
MIT
2021-05-05T12:54:38.000Z
2021-12-17T18:19:13.000Z
Qwen/Qwen-72B
1. YES
2. YES