All Questions

Filter by
Sorted by
Tagged with
0
votes
1answer
49 views

How to solve this equation by Solve?

I have an equation to be solved. But Mathematica does not work for it. I hope the solution x can be expressed as a function of a and b ...
0
votes
1answer
28 views

Solving an equation involving a determinant (including spherical recursive functions)does not compute

I'm trying to solve this matrix to get a resulting function that depends on the variable Q (or if impossible, H3). When I try to to that I get two results: if I try to solve for Q, it doesn't show ...
-1
votes
1answer
54 views

Finding all roots of a function within an interval [duplicate]

I have the following code: ...
0
votes
1answer
88 views

Solving two nonlinear equations in two unknowns

This is my code defining two nonlinear equations. I want to solve them simultaneously. ...
4
votes
3answers
176 views

Finding Root of BesselJ [closed]

When I work on some physical problem I needed to know how to get all of first 100 roots of BesselJ[n,x] function -which is a quasi periodic function-, as a List. I ...
3
votes
2answers
83 views
0
votes
4answers
119 views

Solving an equation involving elliptic integral

Consider the following function: f[θ_] = Integrate[1/(Cot[θ]^2 - Sin[θ]^2)^(1/2), θ]; Now, I want to determine the value of $\theta$ for which say $f(θ)=1$. I ...
8
votes
1answer
319 views

What replaces BesselJPrimeZeros[n, k] in current versions of Mathematica?

In older versions of Mathematica, there was a function called BesselJPrimeZeros used to find the zeros of the derivative of BesselJ function. http://mathworld....
1
vote
0answers
86 views

Evaluate a precision-sensitive function

I want to define a nice function Φ in 3D that is computed as follows $$ \phi (x, y, z) = - z + \frac{\sqrt{32}}{\pi} \sqrt{\cosh \nu - \cos u} \sum_{n = 1}^\infty ...
0
votes
0answers
70 views

Analytic solution to differential equation for fermions

In this paper FermionicOperators, the author solved the following D.E (see eq.($33$)) in the paper $$\Bigg(\partial_r^2 + \frac{6}{r} \partial_r + \frac{1}{r^2}(-|m_l|^2 R^2 + 6 + |m_l| ~ R ~ \gamma^...
1
vote
1answer
64 views

Plotting a variable that is within a hypergeometric function

I kindly ask for help with the following problem. I have two equations. The first one is: 1/(p (1 + (-1 + n) r)) == 1/Hypergeometric2F1[1, k - n, k, q/(-1 + q)] ...
3
votes
1answer
157 views

Hertzian contact mechanics: symbolically calculating the required force for a specific displacement

Consider two parallel Cylinders with Diameters of $R_1$ and $R_2$: The contact width can be calculated from 2D Hertz formula: $$ a=2 \sqrt{\frac{PR}{\pi E_c}} \tag{1}$$ Where $P=\frac{F}{L}$ is ...
0
votes
1answer
63 views

Add more than one condition to my equation

I have the following code to solve for a bunch of n, m e U, but I need different conditions for n=0 and m=n, already explicit in my code, but I don't know how to make it work. I know I have to make it ...
0
votes
0answers
51 views

Solve and Special Functions [duplicate]

How can I use Solve to get the solutions of the following equation? Is it possible? ...
2
votes
3answers
129 views

Problem with C[i] of a second-order nonlinear ordinary differential equation

I'm trying to solve this differential equation (depending on the K0 parameter): ...
1
vote
1answer
112 views

Strange behavior of solution to $- \frac{\partial^2 \psi\left(x\right)}{\partial x^2} - e^{-\alpha x} \psi =0$

Say we have the following equation the following equation (inspired from quantum mechanics with $V\left(x\right) = - e^{- \alpha x}$): \begin{align} \label{eq:first-eq} - \frac{\partial^2 \psi\left(...
6
votes
1answer
872 views

How to solve a Sturm-Liouville problem with Mathematica (or, how to go from the complex to the general *real* solution)?

Let $a>0$ be a constant positive number. I am stuck trying to solve the following regular Sturm-Liouville problem: $$\frac{\mathrm d}{\mathrm d x}((a+x)f'(x)) = -v f(x),\qquad f(0)=f(1)=0$$ where ...
3
votes
1answer
112 views

Zeros of the Hankel function with complex parameter

I'm trying to find the zeros of the Hankel function (the first few will do) of the first kind $H^{(1)}_\nu(z) = J_\nu(z) + i Y_\nu(z)$ for complex argument $z$ but I'm not sure what is the best ...
4
votes
3answers
639 views

NSolve, no output

I want to eventually solve this with these three parameters being given from a list or table. It is not returning a solution, but I know that there is a 0 of this function (from looking at the plot) <...
16
votes
2answers
349 views

Backslide in NSolve in V11.1?

Bug introduced in 11.1.0 and persisting through 11.1.1 In V11.1, NSolve[BesselJ[0, x] == 0 && 0 < x < 20, x] returns no solutions: But in V11.0 (...
4
votes
3answers
165 views

Using the solution to an equation in another function

I am trying to use the solution to $R^2 \left(1-\frac{1}{r}\text{Erf}[r/4]\right)=r^2$ for $r$ in the function Potential$(R)=\frac{1}{R^2}\left(1-\frac{1}{r}\text{Erf}\left(r/4\right)\right)$ and ...
1
vote
1answer
253 views

Finding intersection points from contour plot

The Left hand side of the equation has only real part. But the right hand side has real and imaginary parts. So i am using a contour plot. The intersection of lefthand side and righthand side of ...
0
votes
1answer
125 views

The value of $\sqrt{\frac{\pi }{2}} C(1)$

I'm going through question 5 here, where they ask to approximate the integral $$I=\int_0^a \cos(t^2) \mathrm{d}t $$ with $a=\sqrt{\pi/2}$. This integral can be expressed using Fresnel integrals as ...
7
votes
2answers
922 views

Solving functional equation

Can I use Mathematica to solve a functional equation? For instance how to solve the following functional equation by using Mathematica? $$H(x+1)=xH(x)+\frac{1}{\Gamma(1-x)}$$ Solution is the ...
10
votes
1answer
1k views

Solving quintic in radicals

I need to find an explicit expression in radicals for the real root of the quintic equation ...
1
vote
0answers
106 views

Multiple Roots of Spheroidal Function

I am trying to compute multiple roots of a spheroidal Function (SpheroidalS1). At first, I define function RootsInRange which ...
2
votes
1answer
131 views

Solve equation which involves sum, binomial coefficient and erf

I want to solve the following equation. Unfortunately solve doesn't do the job. Is there any other way or am I doing something wrong? ...
2
votes
2answers
115 views

Help with solving trascendental equations involving Bessel's equations [duplicate]

I'm pretty new at using Mathematica, so I sometimes find errors in stuff so simple I can't seem to find where the error is. I've been trying to solve a trascendental equation that involves a number ...
3
votes
0answers
91 views

Spheroidal Eigenfrequency

I am trying to create a Mathematica function which will calculate the eigenfequencies of a spheroidal cavity. The expressions I use are based both on the book "Spheroidal Wave functions in ...
1
vote
1answer
130 views

A working command for solving a PolyLog equation? (Solve and NSolve don't work)

I need to solve an equation of this form: NSolve[a + x^b + PolyLog[c, x] + PolyLog[d, 1/x] == 0, x] Where $a, b, c, d$ are constants. For the sake of simplicity we can make $a = b = c = d$. Ok I ...
2
votes
2answers
150 views

Using FindRoot to track moving Bessel Functions zeros

Setting up the problem I want to study the common zeros of these two functions: ...
4
votes
4answers
559 views

How to solve equation with variable in integral

Here is the equation I want to solve. [$c$ and $M$ have specified values, and I want the value of $p$.]: $$(2p-c)\int_p^M\frac1{n^2}e^{p-n}\,\mathrm dn=1-\frac{c}{p}$$ For example with $c=0.1$ and $...
1
vote
1answer
48 views

Determine parameter from which on there is no more root for a given function

Let $\gamma>0$ be a real number and $\Phi(r)=\frac{1}{r}-\frac{\pi}{4}\left(H_0(r/2)-Y_0(r/2)\right)$ defined on $[0,\infty)$, where $H_0$ is the Struve function of order zero and $Y_0$ is the ...
1
vote
1answer
189 views

How to solve an iterative integral equation for a function in Mathematica 8.0?

I would like to solve the following iterative integral equation in order to find the functional form of $P_{0}(k)$ numerically and then use it subsequently for the rest of my code: ...
1
vote
2answers
293 views

Solving system of equations with (nested) Bessel Functions

I'm trying to find solutions to a system of equations which include Bessel functions. It feels like the problem for mathematica is that the arguments of the Bessel functions are functions themselves ...
3
votes
2answers
278 views

Solving and Plotting Infinite sums over solutions to transcendental equation involving Bessel functions

I am trying to use Mathematica to plot the following equation $E(q,\Delta)$ vs $qa$, for set values of $ D \Delta/a^2$ and $\bar\rho a/D$. I have looked at other stackexchange posts which deal with ...
1
vote
1answer
190 views

Solving two equations with modified Bessel functions

I am trying to solve two equations with Bessel functions in them, 1) C1*BesselK[0, 3.7268*10^-4*x] == 1.3*10^-6 2) ...
1
vote
1answer
383 views

Finding roots of Bessel function $y=3J_1(x)+xJ_1'(x)$ is returning inaccurate roots. Not Kernel bug [closed]

I can't figure out why Mathematica is returning the incorrect roots. The first five should be 2.9496,5.84113,8.87273,11,9561, and 15.0624 according to my textbook. ...
2
votes
1answer
1k views

Why does the integral not converge?

I am trying to solve for $\Omega$ this nonlinear integral equation: $$1+\dfrac{z}{k^2}-\dfrac{z^2}{K_2(z)} \dfrac{\Omega}{k^3} \displaystyle\int_{1}^{\infty} \gamma^2\, \text{ArcTanh} \left(\sqrt{\...
1
vote
2answers
539 views

Finding roots of a function that includes Bessel functions [duplicate]

I'm fairly new to Mathematica so forgive any stupid mistakes. Here's my function: ...
9
votes
3answers
566 views

Labeling solutions of an Eigenvalue equation involving Bessel functions

I'm solving the Schrödinger equation for a particle in an annular geometry with hard wall boundary conditions and I've reduced it to the following equation: $$J_m(k\,R_1)\,Y_m(k\,R_2) - J_m(k\,R_2)\,...
2
votes
1answer
124 views

Using NSolve for Elliptic Equations over Fundamental Parallelogram in Complex Plane

I'm considering solving elliptic functions over a fundamental domain of the torus with half-periods $\omega_{1}=\pi/2$ and $\omega_{2} = \pi \tau /2$, where $\tau$ is the modular parameter of the ...
3
votes
2answers
513 views

Show Factorial instead of Gamma in the result of RSolve

Now I wanted to solve for a recurring function with RSolve. Here's how I tried: ...
0
votes
1answer
105 views

Implementing AiryAiPrimeZero function

There are some functions implemented in the Wolfram Language related to Airy functions. For example, AiryAi, AiryAiZero or ...
2
votes
3answers
1k views

Find zeros of function in 2 variables

I have two functions $f(r,\phi)$, and $g(r,\phi)$. What is the best way to find the curve in the plane $(x,y)$ or $(r,\phi)$, over which $f(r,\phi)=g(r,\phi)$? I know how to plot it, using ...
15
votes
2answers
495 views

How can I get the solutions of $x^n-x-t=0$ in hypergeometric form?

$x^3-x-t=0$ has three roots that can be expressed in hypergeometric form, for example $$x_1=-1-\frac{t}{2}{_2F_1\left(\frac{1}{3},\frac{2}{3};\frac{3}{2};\frac{27t^2}{4} \right)}+\frac{3t^2}{8} {...
2
votes
3answers
1k views

Solve an equation that include Gamma

I want to solve the following equation Solve[Gamma[1 + x]/Gamma[x - 1/2] + 1 == 0, x] I have answer x=-0.25, but I can not obtain this answer with Mathematica. ...
1
vote
1answer
319 views

How to solve algebra equations containing integration and parameters?

I'm trying to solve two nonlinear algebra equations for two unknown parameters, U and Tf. Since some terms in these equations ...