product of functions

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I just started using SageMath and I am trying to do something simple but I cannot figure it out.

I have a Gaussian function

mu, sigma, x, N = var('mu, sigma, x, N')
P(x) = 1/sqrt((2*pi*sigma^2))*exp(-(x-mu)^2/(2*sigma^2))

and I want to calculate the product of N such functions.

I tried

f = lambda x, N: prod([P for x in range(1, N)])
f(x, N)

and I got the error:

TypeError: unable to convert N to an integer

I works if I choose N to be some number, but I would like to get a symbolic expression output.