Questions on the special mathematical functions implemented in Mathematica.

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6
votes
2answers
285 views

Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
6
votes
0answers
331 views

Reproducing the Integral Definition of the Modified Bessel function

I need to simplify some integral expressions in terms of special functions, such as the modified Bessel function of the first kind. See for example Eq. (5) on this page. Notice that the real ...
2
votes
1answer
287 views

Directional derivative of SiegelTheta

I'm working on a problem where I have to integrate both the Mathematica function SiegelTheta and some of its second order directional derivatives. Using the function works well but something goes ...
1
vote
1answer
399 views

Plotting Fresnel function

I am trying to plot the partial sums and the cesaro means of the function $\sqrt{|x|}$ and for $a_{n}$, I obtained the following code which contains FresnelS. ...
9
votes
2answers
2k views

problem with coloring spherical harmonics

I want to color a spherical harmonics. So I write as follows. ...
8
votes
1answer
1k views

solve an integral equation numerically

I am trying to find a numerical solution for an equation of the form: $$ f(t)=\int_{t_{min}}^{t} {\exp[2 (t^\prime - t)] E(t^\prime) f(t^\prime)} + \int_{t}^{0}{ \exp(t^\prime - t) E(t^\prime) ...
9
votes
3answers
1k views

Multi-Factorial and Series with Triple-factorial terms

Let $n!^{(k)}$ denote a multi-factorial which is defined by $$ n!^{(k)} = \begin{cases} 1 & n \leqslant 0, \\ n, & 0 < n < ...
3
votes
0answers
154 views

Why doesn't Log[Gamma[]] simplify to LogGamma[] where it could?

I have been playing with various equations involving amount of permutations in relatively large sets. Easiest way to look at these is something like Log[10, bignumber!] . Often expressions, even ...
8
votes
1answer
1k views

Implementation of Incomplete Fermi-Dirac Integral in Mathematica

I'm working on a special algorithm to implement a more accurate effective mass calculation for hole carriers in silicon in Mathematica. This rather involved algorithm uses incomplete Fermi-Dirac ...
4
votes
2answers
180 views

LevinRule and SphericalBessels

I'm currently looking at a simplified problem that approximates another problem I'm looking into. In this simplified problem I at least have an analytic integrand and can easily provide all info on ...
10
votes
1answer
701 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 ...
5
votes
2answers
248 views

Solve for $a$ as a function of $\beta$?

I am trying to solve this equation: $$\beta^{-a} \Gamma(a) \sin(a \pi) + e^\beta \beta^{2 a - 1} \Gamma(1 - a) \sin(a \pi) = 0$$ I tried the following: ...
26
votes
1answer
835 views

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 ...
0
votes
1answer
316 views

Iterative way to find roots of confluent hypergeometric function

I am trying to find roots of confluent hypergeometric function and I wonder if I can choose the initial guess by the choice of $\beta$. ...
9
votes
4answers
705 views

Finding the roots of Hypergeometric1F1[]

I am trying to find the roots, λ, for this equation: Hypergeometric1F1[1/4 (2 -  λ /β), n + 1, β] for certain ...
13
votes
1answer
305 views

Extra factors appear when evaluating Euler integrals

Note: this is fixed in version 9. When I perform the double integral in Mathematica, Integrate[(x (1 - x))^z (y (1 - y))^z, {x, 0, 1}, {y, 0, 1}] which ...
3
votes
2answers
282 views
7
votes
0answers
606 views

Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
8
votes
3answers
1k views

Checking if the roots of a function are real

I'm trying to determine if the roots of a function are real. How would you do that? (In particular I'm interested in verifying that the roots of LegendreP[6, x] ...
18
votes
6answers
5k views

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 ...
14
votes
1answer
567 views

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 ...
6
votes
2answers
714 views

Why does Expand not work within a function?

I'm writing this fairly simple function: ...
40
votes
2answers
3k views

What is the difference between a few simplification techniques?

I am trying to understand the difference between Refine, Simplify and FullSimplify, and when ...
12
votes
4answers
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.]. ...
8
votes
1answer
694 views

Hankel Transform integrals won't work in Mathematica

I'm trying to do this integral, which is shown on the Wikipedia page on the Hankel transformation: $$\int_0^{2\pi}\mathrm d\varphi\;e^{\mathrm im\varphi}e^{\mathrm ikr\cos(\varphi)}$$ The answer is ...
4
votes
2answers
216 views

Problem with EllipticE documentation

The complete elliptic integral of the second kind, EllipticE, is defined as, Integrate[Sqrt[1-m Sin[t]^2],{t,0,z}] According ...
31
votes
3answers
763 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 ...