# Legendre_P in symbolic function - recursion error

Hello,

Undergraduate Physics mathemtica->sage convert here trying to use sage for both symbolic substitution to print equations and to plot.

I have the equation `M_y^2 * cos(x)^4 -2*My(x)*sin(x)*cos(x)^3`

and would like to see how this behaves when substituting different associated legendre polynomials for `My^2`

. Code for this:

```
Y_fnc(x,y_max,l,m)=y_max*gen_legendre_P(l,m,cos(x))
f(x,y_max,l,m)=Y_fnc(x,y_max,l,m) * cos(x)^4 -2*sqrt(Y_fnc(x,y_max,l,m))*sin(x)*cos(x)^3
```

Which results in:
```
[...]
File "/home/ian/sage-6.8-x86_64-Linux/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py", line 319, in symbol raise NotImplementedError("symbol")
RuntimeError: maximum recursion depth exceeded while calling a Python object
```

With example line of the truncated output being:
```
File "/home/ian/sage-6.8-x86_64-Linux/local/lib/python2.7/site-packages/sage/functions/orthogonal_polys.py", line 1239, in gen_legendre_P
return sqrt(1-x**2)*(((n-m+1)*x*gen_legendre_P(n,m-1,x)-(n+m-1)*gen_legendre_P(n-1,m-1,x))/(1-x**2))
```

I have also tried to use maxima.assoc_legendre_P but this doesn't work when I try to plot:
Y_fnc(x,y_max,l,m)=y_max*maxima.assoc_legendre_P(l,m,cos(x)) f(x,y_max,l,m)=Y_fnc(x,y_max,l,m) * cos(x)^4 -2*sqrt(Y_fnc(x,y_max,l,m))*sin(x)*cos(x)^3 plot(f(x,1,2,0),0,2*pi)

```
verbose 0 (2716: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 200 points.
```

.

verbose 0 (2716: plot.py, generate_plot_points) Last error message: 'unable to simplify to float approximation'

I can accomplish plotting by defining Python Functions:

edit:

def Y_fnc_py(x,l,m,y_max): return y_max*gen_legendre_P(l,m,cos(x)) def f(x,y_max,l,m): return Y_fnc_py(x,y_max,l,m) * cos(x)^4 -2*sqrt(Y_fnc_py(x,y_max,l,m))*sin(x)*cos(x)^3 plot(f(x,y_max=2,l=1,m=1),0,2*pi)

Works however this will not allow me print f(x,y_max,l=3,m=2) so I can easily write down the equation. So this allows me to plot easily but doesn't display the equation well Help much appreciated thank you

At the end of your question you say "I can accomplish plotting by defining Python Functions ". Could you explain how you did this so that we can understand the problem ?