1-dimensional Gaussian integral \[ \begin{gathered} \int_{-\infty}^{\infty} e^{-x^2} d x=\sqrt{\pi} \\ \int_{-\infty}^{\infty...

Solution Explanation show that, under the (zeroth-order) Hankel transform in the radial variable, \[ \mathcal{H}_0\left[\nabl...

\(\Gamma\) Gamma function - Wikipedia For \(\Re(z)>0\) the \(n\)th derivative of the gamma function is: \[ \frac{d^n}{d ...

Continuity equation: Current density: [1] \[ \boldsymbol{j}=\rho \boldsymbol{v}\quad(1) \] where the direction of \(\boldsymb...

Continuity equation: Current density:[1] \[ \boldsymbol{j}=\rho \boldsymbol{v}\quad(1) \] where the direction of \(\boldsymbo...

This note primarily delves into incompressible flow momentum equation and Surface of water waves and boundary condition and Variational Formulation.

dyadic product There are several equivalent terms and notations for this product: the dyadic product of two vectors \(\mathb...

levi-civita symbol 2-d In two dimensions, the Levi-Civita symbol is defined by: \[ \varepsilon_{i j}=\left\{\begin{aligned} +...