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.)
722
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Radial wavefunction at origin for excited states $|{R_{nl}}^2| (0)$ for quarkonium
I am solving the radial Schrodinger wave equation for quarkonium containing a quark and antiquark. The system is non-relativistic as quarks are charm and bottom which are heavy. The wave equation is ...
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Does $\frac{1}{1-e^{-\frac{1}{e^x}}} - e^x - \frac{1}{2} $ really explode with oscillatory behavior past $x = 15$?
I was looking at the function
$$ \frac{1}{1-e^{-\frac{1}{e^x}}}-e^x - \frac{1}{2}$$
I thought I had reason to believe this tends to 0 as $x$ tends to positive infinity because
$$ \sum_{n=0}^{\infty} ...
- 17.5k
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Mathematica help to check a positive definite matrix
I am new to Mathematica and am trying to check if the following matrix is positive definite with the program. The answer is supposed to be yes because $x > 0$ and $y > 0$ but I don't know how to ...
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Solution to degenerate case of hypergeometric differential equation
I am trying to find two independent solutions of this differential equation: $$x(1-x)y''(x)+\left[\frac d2-\left(d+\frac12\right)x\right]y'(x)-\frac{(d-1)d}{4}y(x)=0,$$ for $0<x<1$.
This is a ...
- 171
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Evaluating Function of Incomplete Elliptic Integrals
I am trying to write Mathematica code that evaluates the following function:
$$
f(\kappa_{yx}, \kappa_{zx}) = 1 + 3 \kappa_{yx} \kappa_{zx} \frac{E(\varphi \backslash \alpha) - F(\varphi \backslash \...
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Partial Differential Equation on a Riemannian Manifold: How to solve complex second order ODE by hand.
I'm working on a project where I discuss using the metric tensor to compute the Laplacian on various Riemannian Manifolds, and how that can aid in solving certain Partial Differential Equations. In ...
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Feeding parameters into a multivar function in Mathematica
I am trying to find an intersection point between a plane and a line. I defined my line as a function of $x,y$ and $z$.
g[x_, y_, z_] := 5 x - 8 y + 2 z - 13
I ...
- 15
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Difference in expected values in Mathematica? [closed]
Could someone explain why I am getting different outputs when I calculate the following two expressions on Mathematica?
First:
...
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what are the branch points and branches of $g(z)=(z+ \sqrt{z})^{1/3}$?
And what if we for example shifted one of the roots, eg $f(z)=(z+ \sqrt{z-3})^{1/3}$?
I already asked a more extensive version of this question here Branch cut/ points for square roots inside cubic ...
- 67
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Branch cut/ points for square roots inside cubic roots- incorrect branching by mathematica or my mistake?
There's a lot of great information here about understanding the branch cuts and branch points of functions of the form ( for example ) $(z^3+1)^{1/2}$, sums of simple roots and products thereof.
...
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Minimizing $\frac{1-c}{1-\frac{(a-b)^3}{(1-a)^2} - \frac{(b-c)^3}{(a-b)^2} - \frac{c^3}{b^2}}$
I am interested in approximating the minimum of
$$\dfrac{1-c}{1-\dfrac{(a-b)^3}{(1-a)^2} - \dfrac{(b-c)^3}{(a-b)^2} - \dfrac{c^3}{b^2}}$$
Subject to $0 < \frac{a-b}{1-a} < \frac{b-c}{a-b} < \...
- 2,457
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Minimizing $\frac{1-\int_{1-\int_{0}^1 F(r)dr }^1 F(t) dt }{1-\int_{0}^1 F(t)^2 dt}$ for increasing function subject to $F(0)=0, F(1)=1$
Let $F:[0,1]\to [0,1]$ be an increasing function with $F(0)=0, F(1)=1$. Define $A(x)=1-\int_{x}^1 F(t) dt$. I am trying to approximately minimize the following ratio across all $F$ (i.e find a lower ...
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Simplifying a particular expression
I have the expression
$$ \frac{x(-c z^{n+1} (-1)^k + c x^{n+1})}{(x-ze^{i \theta})(x - ze^{-i\theta})},$$
where $b$ and $c$ are non-zero complex numbers, $z = \frac{b}{\sqrt{bc}}$ and $\theta = \frac{...
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Closed form expression for an integral
Let $\psi_q(z)$ be the q-DiGamma function defined for a complex variable $z$ with $\Re(z)>0$ as $$\psi_q(z)=\frac{1}{\Gamma_q(z)}\frac{\partial}{\partial z} (\Gamma_q(z))$$
where $\Gamma_q(z)$ is ...
- 910
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Solving a set of implicit equations involving Polylogarithms
I have the following simultaneous equations:
\begin{aligned}
&H(\lambda) = a\, \text{Li}_{3/2}\left(b\frac{H(\lambda)}{F(\lambda)}\right), \; \\&H(\lambda) = c\, \text{Li}_{3/2}\left(d \, \...
