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Reading the book "Fundamentals of Renewable Energy Processes I came across an equation I am not sure how to read. The equation is: $$J_0=q\frac{4\pi}{h^3}mk^2T^2exp(-\frac{q\phi}{kT}) $$ I am looking at this and I am not sure how to read this. Is this equivalent to $$J_0=q\frac{4\pi}{h^3}mk^2T^2e^{(-\frac{q\phi}{kT})} $$ or am I reading it wrong?

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Yes. The notation $exp(a)$ and $e^a$ are the same, although I have absolutely no idea what those variables are.