# Tagged Questions

Questions on the special mathematical functions implemented in Mathematica.

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### About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...
290 views

### When does the real part of Zeta vanish on the critical line?

This seems to be a quite a simple problem but I cannot make it work. I am trying to find all values within a given range for which the real part of the Zeta ...
5k views

### What is the difference between a few simplification techniques?

I am trying to understand the difference between Refine, Simplify and FullSimplify, and when ...
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### Why does Expand not work within a function?

I'm writing this fairly simple function: ...
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### Replacing gamma at half integers by double factorial

It is well-known that for any positive integer $n$ the equality $\Gamma(n+\frac12)=\sqrt\pi\,(2n-1)!!/2^n$ holds, where $!!$ stands for the double factorial. I am using ...
2k views

### Numerical underflow for a scaled error function

I calculate scaled error function defined as f[x_] := Erfc[x]*Exp[x^2] but it can not calculate f[30000.]. ...
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### Visualizing vector spherical harmonics

I have painstakingly derived the vector-spherical harmonics $\mathbf{V}_{J,\,M}^\ell(\theta, \phi)$, which are the generalization of ordinary spherical harmonics $Y_\ell^m(\theta, \phi)$ to vector ...
240 views

### Precompiling a Whittaker function

Is there a way to speed up the evaluation of special functions in Mathematica? I am particularly interested in the Whittaker W function. For instance, the following piece of code: ...
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### How to simplify an expression with special functions to zero

The following is a well-known Bessel function identity: $$J_{-n}(z)=(-1)^n J_n(z),\qquad n\in\mathbb Z$$ To check this, I used the following code and the result is as what I expected. ...
3k views

### Series expansion in terms of Hermite polynomials

I am trying to expand a polynomial in terms of orthogonal polynomials (in my case, Hermite). Maple has a nice built-in function for this, ChangeBasis. Is there a ...
410 views

### Find asymptotics of $\sum\limits_{i=0}^{n/3} 2^i \binom{n-i-1}{\frac{2n}{3}-1}$

I have an expression 2^n / Sum[ 2^i Binomial[ n - i - 1, 2n/3 - 1], { i, 0, n/3}] ...
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### Incorrect result from Integrate

Bug introduced in 8.0 and fixed in 10.0 I attempted to calculate the following integral: ...
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### Incorrect results for elementary integrals when using Integrate

There is a rather simple integral ($K_0$ is the 0-th order MacDonald function) $$\int_0^\infty e^{-x \cosh\xi}\, d\xi = K_0(x)$$ which mathematica cannot solve. This even though the documentation ...
946 views

### Is my expression too complicated for FullSimplify or am I doing something wrong?

I have a messily defined function $v(h, w)$ with $h, w \in \mathbb{R}$ and with a removable singularity at $h=1/2$, and I am trying to prove some of its properties using Mathematica. In particular I ...
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### Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
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### Teaching Mathematica more about DiracDelta and KroneckerDelta

As the documentation and some experimentation indicates, Mathematica contains little information about representations of the DiracDelta and ...
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### Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ?

Bug introduced in 8.0.4 or earlier and persists through 10.4. I am trying to evaluate this integral numerically $$\int_0^{\infty } J_0(q R) \tanh(q) \, \mathrm{d}q$$ for large values of $R$. ...
3k views

### problem with coloring spherical harmonics

I want to color a spherical harmonics. So I write as follows. ...
263 views

### How to plot the result of this singular integral?

Please I open a new post here after this one : http://mathematica.stackexchange.com/a/59203/10158 Now I want to plot the function $f(a,b)$ as a function of $b$ for different values of $a$ : $a=0.5$ , ...
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### Puzzled by Assumptions [duplicate]

I don't know if this has already been discussed. Integrate[BesselJ[2 m + 1, x], {x, 0, ∞}, Assumptions -> m ϵ Integers] ...
490 views

### Assigning an analytical approximation to the error function erf(x)

Working with some iterative integral equations, I have Gaussian density functions involved therein. Integrating the Gaussian function I obtain the error function. When I take the second integration, ...
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### Hypergeometric function with a matrix argument

I am looking for the evaluation of a Hypergeometric function with a matrix argument as for example in Koev and Edelman or as showcased in this Wikipedia article. From what I understand from ...
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### Why is the Spherical Bessel Function acting strangely at this point?

I'm doing some computation that requires the use of Spherical Bessel Functions of the 1st kind, at high orders and values. So, I managed to find this, while running it over a wide range of values. I ...
254 views

### Find all roots of a function with parabolic cylinder functions in a range of the variable

I want to find all roots of a function involving Parabolic Cylinder Functions. In what follows, I define 2 variables $\xi1$ and $\xi2$, which in turn depend on $\omega$. My function is then defined as ...
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### Peirce's quincuncial projection

The Peirce quincuncial projection is the cartographic projection of a sphere onto a square. In short, I would like to see it implemented in Mathematica. Here is my code: ...
938 views

### Is there a Mathematica API for the functions.wolfram site?

Is there a Mathematica API for the functions.wolfram site? If there's not, has anyone implemented a web scraper for it? For example it would be nice to be able to access http://functions.wolfram.com/...
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### Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
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### Number of divisors visualized with the QPochhammer function, how to improve performance of code?

I have this code that is originally Jeffrey Stopple's code for the Riemann zeta function in the complex plane. Because I discovered yesterday that the number of divisors can be generated with the $q$-...
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### Visualizing vector-spherical waves

This is a follow-up question to this one on visualizing vector-spherical harmonics. This time, I would like to visualize the vector spherical waves (including the radial dependence). The functions ...
462 views

### How to enlarge Mathematica's knowledge about certain functions?

I'm often troubled with the following task. I need to carry out symbolical computations involving certain special functions. Let me take as an example Barnes gamma-function. It is included in ...