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Recently Referred Formulae


\phi(x) = f(x)   \lambda \int_a^x K(x,t)\,\phi(t)\,dt

\phi(x) = f(x)   \lambda \int_a^b K(x,t)\,\phi(t)\,dt
{\rm d}y &=& \frac{1}{x}{\rm d}x - \frac{1}{2x^2} ({\rm d}x)^2\\
 &=& \frac{1}{x}(\mu x {\rm d}t   \sigma x {\rm d}W_t) - \frac{1}{2x^2}(\sigma^2 x^2 {\rm d}t)\\
 &=& (\mu - \frac{1}{2}\sigma^2){\rm d}t   \sigma {\rm d}W_t
{\rm d}v &=& ae^{at}u {\rm d}t   e^{at}{\rm d}u\\
&=& ae^{at}u {\rm d}t   e^{at}(-au{\rm d}t - \sigma{\rm d}W_t)\\
&=& -\sigma e^{at}{\rm d}W_t
{\rm d}y(t) &=& \frac{\partial g}{\partial t}{\rm d}t   \frac{\partial g}{\partial x}{\rm d}x   \frac{1}{2}\frac{\partial^2 g}{\partial x^2}({\rm d}x)^2