A powerful search engine for mathematical formulas with LaTeX support
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Mathematics
The limit definition of the exponential function
A definition of the exponential function that has found application in numerous approximation schemes is \(e^x = \lim_{y\to\infty} \left(1+\frac{x}{y}\right)^y\).
Physics
The heat equation
The heat equation, \(\frac{\partial \varnothing}{\partial t} = D \nabla^2 \varnothing\), uses the Laplacian of \(\varnothing\) to express diffusion through a medium.
Physics
The Schrödinger equation
The Schrödinger equation, \(i \hbar \frac{\partial \Psi}{\partial t} = \hat H \Psi\), is a partial differential equation for the wave function \(\Psi\) of quantum mechanics.