# Tagged Questions

**2**

votes

**1**answer

77 views

### M-Wright function asymptotics

Let $M(z;\nu):= \frac{1}{\pi}\sum_{n=1}^{\infty} \frac{(-z)^{n-1}}{(n-1)!}\Gamma(\nu n)\sin(\nu n\pi)=\frac{1}{2\pi i}\int_{\text{H}_a}\exp(\sigma -z\sigma^{\nu})/\sigma^{1-\nu} d\sigma$, ...

**9**

votes

**1**answer

817 views

### Has anyone seen this series?

I come across the following infinite series.
$$
\sum_{n=1}^{\infty} \frac{t^n}{n!\: n^{a}}, \quad\text{for $t>0$ and $a>0$}.
$$
In particular, I am interested in the case where $a=1/4$.
...

**1**

vote

**0**answers

224 views

### Whether does the following equation have only one finite zero?

Dear MOs,
Here is a calculus problem which bored me for sometime. Let $a>0$ and $b<0$ be fixed.Define the following function (EDIT: Following the comment by Barry Cipra, you may only consider ...

**2**

votes

**2**answers

244 views

### Computing hypergeometric function of matrix argument

In the context of the Bingham probability distribution the ${ }_1F_1$ hypergeometric function of matrix argument naturally arises as a normalization constant of the probability distribution function. ...

**9**

votes

**2**answers

482 views

### The fraction of the sphere a fixed distance from a subspace

The following problem has a beautiful geometric interpretation in terms of the proportion of points on the Euclidean sphere in $\mathbb{R}^d$ that lie at least a certain distance away from a ...

**2**

votes

**0**answers

120 views

### Are numbers $h_{r,s} = \sum_{k} P(r;s;k) \frac{1}{n^{2k}} \bigg(1-\frac{1}{n}\bigg)^{n-2k}$ irrational?

I asked this question on MSE and Mike Spivey gave an insightful answer. I decided to put it here nevertheless in case someone else gets interested. If this violates rules on MO, please let me know, ...

**1**

vote

**1**answer

312 views

### Product of densities of a wrapped normal distribution

The density of a wrapped normal distribution is given by
$$\frac{1}{\sigma \sqrt{2\pi} }\sum _{k=-\infty }^{\infty }\text{Exp}\left[\frac{-(\theta -\mu -2\pi k)^2}{2\sigma^2}\right]$$
Considering two ...

**1**

vote

**1**answer

214 views

### A uniqueness proposition involving Erf, the error function

This is a generalization of a previous MO question, "Reducing system of equations involving Erf, Error Function".
Consider the system of equations:
$$1/2 + {\rm Erf}(x) - \alpha {\rm ...

**3**

votes

**2**answers

581 views

### Reducing system of equations involving Erf, Error Function

I have a system of equations:
$$1/2 + {\rm Erf}(x) - {\rm Erf}(\frac{x+y}{2})=0$$
$$-1/2 + {\rm Erf}(y) - {\rm Erf}(\frac{x+y}{2})=0,$$
Where $x \le y$ and ${\rm Erf}$ is the Error Function.
By ...

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votes

**4**answers

1k views

### Estimating the probability that one Poisson RV is larger than another

Let $X$ and $Y$ be Poisson random variables with means $\lambda$ and $1$, respectively. The difference of $X$ and $Y$ is a Skellam random variable, with probability density function
$$\mathbb P(X - Y ...

**1**

vote

**3**answers

2k views

### Integral over error function and normal distribution

Help me understand why
$\int_{-\infty}^{\infty}\frac{1}{2}[1+\operatorname{erf}(\frac{\theta-x}{\sqrt{2q^2}})]\frac{1}{\sqrt{2\pi\sigma^2}}{\exp(-\frac{(x-\mu)^2}{2\sigma^2})}dx \approx ...

**2**

votes

**0**answers

460 views

### Generalization of repeated error function integral

Is there a name for the following integral?
$f(x, y, n) = \int_y^\infty (t - x)^n \exp(-t^2) dt$
The parameter $n$ is positive. The first priority is integer $n$, but more generally the case of ...