Limit and summation in Python-CodePudding

I am trying currently to calculate the limit of the following formula:

I tried the following code:

nsum(lambda k: ((x)**(2k))/fac(2k), [0, inf])

where x = np.pi/2 it returned the following message:

 File "C:\Users\AppData\Local\Temp/ipykernel_14/335.py", line 3
    nsum(lambda k: ((-1)**2*(x)**(2k))/fac(2k), [0, inf])
                                   ^
SyntaxError: invalid syntax

I tired this too:

sym.limit((np.pi/2)**(2k))/fac(2k), k, sym.oo)

I got the same error:

File "C:\Users\AppData\Local\Temp/ipykernel_14/40.py", line 1
    sym.limit(((np.pi/2)**(2k))/fac(2k), k, sym.oo)
                                    ^
SyntaxError: invalid syntax

I could not figure out where my problem lies, any idea would be appreciated.

CodePudding user response：

With Python, multiplication needs to be written explicitly. In your case, you need to write 2*k.

Edit: it is clear that this is your first time with Python and the distinction between numerical and symbolic libraries. Here, I'm going to discuss SymPy and the way I would approach your problem:

from sympy import var, Sum, pi, factorial, limit
# create symbols n and k
var("k, n")
# create a symbolic expression.
# NOTE: I have replace the upper limit n with infinity
expr1 = Sum((pi / 2)**(2 * k) / factorial(2 * k), (k, 0, oo))
expr1.doit()
# output: cosh(pi/2)

# If you wanted to compute the limit of the original expression:
expr2 = Sum((pi / 2)**(2 * k) / factorial(2 * k), (k, 0, n))
limit(expr2, n, oo)
# It throws an error!