# Questions tagged [approximation]

For questions that involve concrete approximations, such as finding an approximate value of a number with some precision. For questions that belong to the mathematical area of Approximation Theory, use (approximation-theory).

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### Gaussian integral: $\int_{-\infty}^{\infty} x^2\left\{ \Phi (a + b x) \right\}^2 \phi(x) \mathrm{d}x$

Is there an analytic solution for the following integral? $$I = \int_{-\infty}^{\infty} x^2 \left\{ \Phi (a + b x) \right\}^2 \phi(x) \mathrm{d}x,$$ where $\Phi(\cdot)$ and $\phi(\cdot)$ are the cdf ...
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### How to use the Backwards Euler Method

Given the ODE $\frac{dy}{dt} = f(t,y)$ and the function $f(y) = -y^3$, with the initial condition $y(0)=1$, I want to use the backward Euler Method with $h = \frac{1}{2}$, combined with the Newton-...
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### Confusion about factorial $\dfrac{(N!)^2}{(2N)!}$

I am confused with the expression $\dfrac{(N!)^2}{(2N)!}$. Suppose we write $(2N)!=p_1^{\alpha_1}p_2^{\alpha_2}\dots p_\ell^{\alpha_\ell}$ and by Hardy-Ramanujan theorem that states that almost all ...
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