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# Questions tagged [closed-form]

A "closed form expression" is any representation of a mathematical expression in terms of "known" functions, "known" usually being replaced with "elementary".

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### Extending differential form from a submanifold to a closed form

I am in $R^4$ in coordinates $x,y,z,t$. Can I extend an arbitrary 3-form defined only at points of the line $x=y=z=0$ to a closed 3-form in a neighbourhood of the line. In fact my question is only ...
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### Integrable subbundle

Let $D\subset TM$ is a integrable smooth regular subbundle and $f_{1},...f_{k}$ is smooth local frame for $Ann(D)$. Why $\omega=f_{1}\wedge ....\wedge f_{k}$ is closed form?
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### Closed-form solution for $\int_{0}^{\pi/4} e^{-(n^2\sec^2x)/2}\,dx$
Is there a closed form solution for the following integral $$\int_{0}^{\pi/4} e^{-(n^2\sec^2x)/2}\,dx$$ for $n>0$ ?