Questions tagged [mathematica]
For questions concerning the popular computational software program published by Wolfram Research. (Note: you are more likely to get quicker and more accurate response if you ask the question on their user forum or on the Mathematica Stack Exchange site.)
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Extracting coefficients from falling factorial form in Mathematica
I have a polynomial in falling factorial form, i. e.
$-x+7(-1+x)x+6(-2+x)(-1+x)x+(-3+x)(-2+x)(-1+x)x$.
Now i want to extract the "outermost" coefficients $\{-1,7,6,1\}$. I have this code to ...
- 141
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Logarithmic Function Calculation in Mathematica
I find these results in the evaluation of the logarithms that only differ in the sign $-$ I do not understand why in the first case $\operatorname{Log}[x+1]/8$ is not returned as an answer.
5
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Optimal length of rope for sliding across a gap
I'm trying to solve a physics problem that I heard ~10 years ago in undergrad that was casually posed to me without a solution in mind; it has been bothering me ever since! Please let me know if this ...
- 252
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Analysis of a sequence based on ratios of floors of consecutive powers of a real value
I am currently interested in the following sequence:
Fix a number $x$, and define a sequence $(a_n)_{n=0}^\infty = \lfloor x^n \rfloor$ and $(b_n)_{n=0}^\infty = \frac{a_{n+1}}{a_n}$
With a little ...
- 399
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Definite Integral involving polynomial and Meijer G-function
I am trying to solve the following integral involving Meijer-g function
$\int_0^{\infty} \left(\varrho x + \nu\right)^{p+\frac{1}{2}-\frac{k}{2}} G_{1,3}^{3,0}\left(\begin{matrix} \frac{\...
- 31
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Fourier transform of incomplete gamma function
Ultimately I am interested in the Fourier transform of
$$
e^{-i\zeta}(-i\zeta)^{-2\epsilon}\Gamma(2\epsilon,-i\zeta)
$$
in a series expansion around $\epsilon=0$, so to first order in
$$
\lim_{\...
- 133
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Uniform initial conditions make Fokker-Planck/Kolmogorov Equation boundary conditions inconsistent
When considering the time evolution of a distribution over a state variable $x$, one of the cases that seems fundamental is when knowledge about $x$ begins uniform. However, modelling the process as ...
- 19
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Software packages to compute finite type invariants of Polygonal Knots
Assume I have a polygonal knot, $K$, represented as its set of vertices $\{\mathbb{v}_i| \mathbb{v}_i\in\mathbb{R}^3\}_{i=1,...,n+1}$, where $n$ is significant, let's say $100<n<500$.
Which ...
- 51
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Difficulty in computing integral
I am currently struggling with computing the following integral (as a whole). First, I define the following function.
\begin{equation}
f(q) = \frac{840q + 190 q^3 + 93 q^5 - 15\sqrt{4+q^2}(28+4q^2 + ...
- 257
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Solving Diophantine Equation in Macaulay2
I have to write a function which solves the diophantine equation $p(s)x^2 = q(s)$ (in $x$) where $p,q$ are integers polynomials in $s.$ This is doable since $p(s) \mid q(s)$ has only finite solutions (...
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Reduce $\frac{d^{n-1}}{dw^{n-1}}\frac{4^{-n/{\sqrt w}}}{\sqrt w}\Big|_1=\frac1{\sqrt\pi}G^{3,0}_{1,3}\left(^{3/2-n}_{0,1/2,1/2};(\ln(2)n)^2\right)$
In this
answer to Is there any valid complex or just real solution to $\sin(x)^{\cos(x)} = 2$?,
one must calculate $$\frac{d^{n-1}}{dw^{n-1}}\left.\frac{4^{-\frac{n}{\sqrt w}}}{\sqrt w}\right|_1=\...
- 12.4k
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Simulation of a pendulum on a spinning Disk
I don't know if this is the right place to ask this Question, but I have previously asked a similar question where i asked how to write a simulation on this phenomenon. I got a great answer with a ...
- 119
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Need help in implementing q-SeriesToq-Product in Mathematica
In Mathematica Guidebook for symbolic computations (https://www.amazon.com/dp/0387950206/wolframresearch-20), in the Exercises, 30 (c)(p. 359), there is a question:
I have no clue how to implement ...
- 23
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A question regarding asymptotics in mathematica
I am trying to see the asymptotics of the Var function as below, from the plot it seems it goes to $-\infty$, however, I also calculate its asymptotics which gives me a positive $+\infty$.. Why could ...
- 1,042
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Mathematica PDE solving
I'm new to Mathematica and have never solved a PDE before. I tried to follow a textbook to get equation 4, but got something different with Mathematica (I got $(4\pi Dt)^{1/2}$ instead of $(4\pi Dt)^{...
- 169