# Tagged Questions

**4**

votes

**1**answer

384 views

### 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 ...

**4**

votes

**1**answer

415 views

### Is there a closed form expression/series expansion for $\int_{\epsilon-i\infty}^{\epsilon+i\infty} e^{az+b^2z^2}\Gamma(z)\Gamma(1-z)dz$ ?

I've been trying to find a closed form expression/series expansion for the following integral without success:
$$F(a,b)=\int_{\epsilon-i\infty}^{\epsilon+i\infty} ...

**8**

votes

**2**answers

481 views

### Rain droplets falling on a table

Suppose you have a circular table of radius $R$. This table has been left outside, and it begins to rain at a constant rate of one droplet per second. The drops, which can be considered points as they ...

**0**

votes

**0**answers

182 views

### Evaluating the integral $\int_{a}^{+\infty} \frac{\exp(-bx)}{x+c} Ei(x) dx$

I'm trying to evaluate or simplify this integral:
$$I_{a,b,c} = \int_{a}^{+\infty} \frac{\exp(-bx)}{x+c} Ei(x) dx $$
with $a,b,c \in \mathbb{R}_+^*$.
and $ Ei(x) =\int_{-\infty}^{x} ...

**0**

votes

**1**answer

229 views

### derivative of a special function in integral form

What is the derivative of $Q_m\left(\frac{\alpha}{x^a},\frac{\beta}{x^b}\right)$ with respect to $x$, i.e,
$$\frac{\partial}{\partial x}Q_m\left(\frac{\alpha}{x^a},\frac{\beta}{x^b}\right),
\quad
...

**2**

votes

**1**answer

330 views

### 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, ...

**1**

vote

**1**answer

155 views

### 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 $D \subset \mathbb{R}^n$ ...

**1**

vote

**3**answers

1k views

### 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 ...

**2**

votes

**1**answer

449 views

### 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 ...

**0**

votes

**1**answer

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 ...

**0**

votes

**0**answers

479 views

### 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 ...

**4**

votes

**1**answer

2k views

### 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 $w$ ...

**0**

votes

**1**answer

940 views

### 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 ...