# Tagged Questions

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### Identity involving Fresnel integrals

In the paper E. Mehlum, Appell and the apple (nonlinear splines in space), Technical Report No. 1676 (1981), Central institute for industrial research, Oslo (reproduced in the book Mathematical ...
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### A Bessel integral

Today I came across the integral $\int_a^\infty e^{-bx} I_n(x) dx$ where $I_n$ is the modified Bessel function of the first kind. There is a solution for $a=0$, provided in Gradshteyn and Ryzhik, ...
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### Integrating with sub-level sets

This is a simple question, and I'm sure it was a homework assignment at some point (assuming it's true) but it's one that I'm puzzled over. Suppose I have a compact domain $D \subset \mathbb{R}^n$ ...
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### How do you calculate the solid angle of a rectangular, axis aligned section of a surface defined by a two dimensional function?

I have $f(x,y) = \frac{1}{2} (1 - x^2 - y^2)$, which is a paraboloid centered around the origin (plot). Now I want to calculate the solid angle (with the origin as the viewpoint) of the surface area ...
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### Integral and limit

During my research this integral has shown up $\frac{1}{2T} \int_{-T}^T \left( 1 - \frac{|\tau|}{T}\right)e^{-\alpha\tau^2}\cos(2\pi f_0 \tau) d\tau$ I tried to solved by taking the real part of a ...
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904 views

### Time scale calculus vs Lebesgueâ€“Stieltjes calculus

About the same time, it seems, as I asked this question, a new post appeared on the wikipedia discussion page for Time scale calculus which suggests the Time scale derivative (aka Hilger derivative ...
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### Integrating the product of two functions one of which has a positive non-integer power

I'm looking to integrate several functions having the form $\int_0^T \frac{ sin(\omega \tau) }{\omega} \tau^{2H} d\tau$ where $2H \ge 0$ but may not be an integer. I'd like to know if the machinery ...
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### Inverse of a function defined by an integral

Hi, I have a function defined by an integral as follows. $$z=f(w) = \int_0^w \frac{(\zeta-a_1)^{\alpha_1}(\zeta-a_2)^{\alpha_2}...}{(\zeta-b_1)^{\beta_1}(\zeta-b_2)^{\beta_2}...}\ d\zeta$$ where $w$ ...
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### Modified Dirichlet function Darboux integrable on [0,2]?

Hi, Given this modified Dirichlet function: f(x) = 0 if x is in Q, else f(x) = x. I am wondering if this function is Darboux integrable on the interval [0, 2]. I managed to show that every lower ...