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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1answer
31 views

Show that when applying these substitution rules the result is an alternating sum with binomial coefficients in the numerators.

The following is Mathematica code. I apologize but I don't know how to write it more clearly. B1 = ReplaceAll[A1, x1 -> 1/A2]; simply means to take ...
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1answer
73 views

How to calculate the following expectation and variance?

Given $$X_1 \sim N(\mu_1, \sigma_1^2),$$ $$X_2 \sim N(\mu_2, \sigma_2^2),$$ $$X_1 \mathrm{\ and\ } X_2 \mathrm{\ are\ independent}.$$ and $$Y = \max(\max(X_1,0) + X_2, 0),$$ find $$E(Y) \mathrm{\ \ ...
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0answers
53 views

Riemann Prime Counting Function correction/pairing terms by Mathematica

Riemann Prime Counting Function: The second correction/paring terms: I tried to use Mathematica function LogIntegral to plot this second correction/paring terms, for example, when I only include the ...
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31 views

How can I reduce the error estimate of numerical integration in Mathematica?

Before introducing the integral I want to go through some definitions. Define triangles $T_1$ and $T_2$ by the points $\{a,b,c\}$ and $\{d,e,f\}$ respectively. Define $$D(u,v,x,y) = sign(\det (y-u,y-v,...
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0answers
38 views

Solving coupled integral equations

I would like to solve coupled integral equations of following form: $$ \begin{cases} f(0,n) = 1 + \displaystyle\int\limits_{0}^{\infty} K(n,p)f(1,p)dp \\ f(1,n) = g(n) + \displaystyle\int\limits_{0}^{...
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1answer
75 views

How did the author solve this integral?

I have the following spherical density distribution: $\rho(x, z) = \frac{1}{\sqrt{x^2 + z^2}\left(1+\sqrt{x^2+z^2}\right)^2}$ which I have broken into a "line of sight" dimension $z$ and a &...
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0answers
23 views

How can I solve this set of complex integral equations on Wolfram/Mathematica?

I need to evaluate the complex line integral in the following equation: $$f(z) = \int_0^z \zeta^{-3/4}(\zeta-a)^{-1/2}(\zeta-1)^{-1/2}d\zeta,$$ where $a$ is determined from the equation: $$\int_0^a=-...
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1answer
58 views

How can I evaluate this complex integral equation on Wolfram?

I need to evaluate the complex line integrals in the following equation: $$g(z)=\frac{\int_0^z\zeta^{-5/6}(\zeta-1)^{-1/2}d\zeta}{\int_0^1\zeta^{-5/6}(\zeta-1)^{-1/2}d\zeta}.$$ Can someone advise me ...
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0answers
15 views

How to label different plots on one graph

I need to sign each plot separately, but I don’t know how to do it. PlotLabel signs all of them above the y axis
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12 views

Any way to remove overlapping textures?

I have used Graphics3D to create two cubes in 3d, and the faces of one line up with the faces of another. This creates a strange overlapping effect which glitches between the two colors chosen for ...
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0answers
59 views

$x_1^2+x_2^2+x_3^2+…x_{10}^2 \leq1$ Do I use the Mathematica QuasiMonteCarlo method wrongley?

I want to find the volume of the multisphere restricted by $x_1^2+x_2^2+x_3^2+...x_{10}^2 \leq1$, by using NIngtegrate and the QuasiMonteCarlo method. I start with dim = 10 with the expression ...
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3answers
87 views

Is $M^TM=I$ not the same as $\mathbf{v}^TM^TM\mathbf{v}=\mathbf{v}^T\mathbf{v}$???

I define a function $f[\mathbf{v}]$ as follows: $$ f[\mathbf{v}]=\mathbf{v}^T\mathbf{v} $$ I am now interested in a group of linear transformation $M$ ($n\times n$ matrices) which leaves the ...
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2answers
22 views

Numerical solution of a linear differential equation with non-constant coefficients

I'm trying to solve the following linear differential equation with non-constant coefficients involving algebraic functions. $\frac{d \phi}{d t}+\frac{ \left(\Delta ^2 \tau ^2-4 i \tau \sqrt{\Delta ^...
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0answers
111 views

Solving a difficult integral

I have been stuck on the following integral for some time: $$ I = \int^{2 \pi}_0 \mathrm{d}\theta \frac{\cos \theta\left(x + \Delta\cos\theta\right)}{\sqrt{k + \left(x + \Delta\cos\theta\right)^2}} \...
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0answers
22 views

Error in Taylor series using Mathematica

How many terms should be used in taylor series expansion of the function f(z) = e^z around z = 0 for a specific value of z = 30 + 30 i to get an error of less than 0.05 using Mathematica? ...
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1answer
104 views

Relationship between bitwise XOR and the equations [closed]

I am studying bitwise XOR. If a, b, c are integers ranging from 0 to 18,446,744,073,709,551,615, I belive the following work for both $=$ and $\neq$: $1.\forall a,b,c(a=b\to a \oplus c=b \oplus c)$ ...
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10 views

How to solve following wave equation?

Use the CTCS scheme with X2-X1=1/3 and t2-t1=1/5 to solve the wave equation Utt(x,t)=Uxx(x,t) with the boundry conditions: U(0,t)=U(1,t)=0 0<=t<=0.6 U(x,0)=(3^1/2)sin(pi....
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0answers
17 views

How to calculate $\frac{\partial tr(XS^T(SS^T+\Lambda)^{-1}SX^T)}{\partial \lambda_i}$ where $\Lambda=diag\{\lambda_1,…,\lambda_n\}$?

How to calculate $\frac{\partial trace(XS^T(SS^T+\Lambda)^{-1}SX^T)}{\partial \lambda_i}$ where $\Lambda=diag\{\lambda_1,...,\lambda_n\}$? $X,S$ are all known. I have this problem when I read paper[1]...
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0answers
21 views

Converting semidefinite program into standard form linear program

I'm new to semidefinite programming and I'm having trouble computing what I think is a fairly simple semidefinite linear program. I need to maximize $$\mathrm{Tr}[H X]$$ subject to some linear ...
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1answer
23 views

Solving linear recurrence relation problem.

Steve borrows 2500 dollars, at 12 percentage compounded monthly, to buy a new 4k LED tv. If the loan is to be paid back over two years, what is his monthly payment? Steve pays back the same amount ...
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1answer
40 views

Determine the number of $n$-digit quaternary $\{0,1,2,3\}$ sequences $a_n$ in which there is never a $3$ anywhere to the right of a $0$. [closed]

Determine the number of $n$-digit quaternary $\{0, 1, 2, 3\}$ sequences, $a_n$ in which there is never a $3$ anywhere to the right of a $0$. 20213 is thus a forbidden string of length 5. What is the ...
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1answer
25 views

Inverse of DiracDelta at 0 is 99/5?

When using Mathematica I've found an interesting result. InverseFunction[DiracDelta][0] == 99/5 (* returns True *) Or the inverse function of the DiracDelta ...
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1answer
26 views

Difficulty with solving system of differential equations with mathematica (new ot mathematica). [closed]

I am able to find a general solution to the following system of differential equations when I use this code in Mathematica: ...
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1answer
23 views

How to write a function that describes a thin spherical shell?

How can we define a 3D function where for all input values of $(x, y, z)$ for $f(x,y,z) = 0$ or approximately close to zero except for where the location of a spherical shell is located. The ...
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1answer
33 views

Using Mathematica to solve a nonlinear system of equations

I'm looking for some sets of solutions for this nonlinear system. I only have to respect the conditions, getting numerical values to use for another thing: $$\begin{align} \delta_i &> 10 |\...
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0answers
19 views

Implement the Newton iteration method for multivalued vector functions

I need to implement the Newton Iteration method for multivalued vector functions. I have this differential equation that I have to solve $$\frac{dA}{dt} - \epsilon \frac{3i}{2} \lvert A \rvert^2 A - \...
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0answers
30 views

Recurrence, checkboard 2xn

Good day, I am finding out the recurrence relationship for a checkboard 2xn. I got 1-squares(1x1) and L shape, 3-squares to choose from to cover the table. n>=1 So a0= 1 since its just two 1-...
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1answer
34 views

Trianlge area and minimum value using Mathematica.

A triangle has two of its corners in (3.052 , 0 , 1.456), (0 , 3.052, 1.456), and the third of the curve in the room consisting of all points (3.052 , 3.052, a ^ 2 + 1.456), where a is a real number. ...
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0answers
33 views

Integrate special function

I have the following integral $$ \int_a^b e^{\alpha_1 x + \alpha_2 x^2 + \alpha_3 e^{-\beta x}} dx, \\ \text{where} \, \alpha_1, \alpha_2, \alpha_3 \,\text{and} \, \beta \, \text{are constants} $$ I´...
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1answer
39 views

Proving a shift transformation theorem with taylor series [closed]

I need to prove a transformation theorem $T(ψ(x)) = (e^{hD})*ψ(x)$ and use Taylor series to do this task. It is known that $T(ψ(x)) = ψ(x + h)$ and $D$ is a derivatation. I have no idea, how to start ...
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0answers
20 views

FindRoot of a function

I am trying to find root of this function using Mathematica but I think the value I get is incorrect, can anyone advise me on this
2
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1answer
29 views

Zero equivalence in computer algebra systems

Testing whether an expression (say, on the real or complex numbers), with or without variables, is known to be difficult. There is an semi-algorithm by Daniel Richardson to solve it for the exp–log ...
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0answers
4 views

Simulating Probabilistic Behaviour

I am trying to develop a code in the Mathematica program to simulate the problem below: I need to run 1,000,000 simulations to determine the mean score for throwing five darts I am having difficulty ...
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3answers
63 views

Why does Mathematica / Wolfram Alpha gives 2 different answers for these 2 queries?

I was assigned to find the integral of this expression: $$ \int\frac{-5x^3+3x^\frac{3}{2}-2x^2-5x + \frac{3}{\sqrt x}}{x^2+1}\mathrm{d}x$$ I did: $$ = \int\frac{-5x(x^2 + 1)}{x^2+1} \mathrm{d}x + \...
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0answers
22 views

Checking that the Cahn-Hilliard equation has solution lattice as in articles and books : but it doesn't work

I'm reading (for instance here ) that the Cahn-Hilliard equation has soliton-lattice solutions : But when I try to check that with Mathematica : ...
2
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1answer
52 views

On simplifying large exponential equations

I'm working on undergrad research in fractal geometry and have to prove certain functions are decreasing, one of which is $$g(x) = \frac{\left( \frac{2^m-2}{2^m-1}+ \frac{1}{2^m-1}\left(\frac{1}{2^m}...
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0answers
10 views

Record the set in the diagram using operations

Can you help me Record the set in the diagram using operations I will be happy for your help. Chart images enter image description here
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0answers
12 views

How to count outputs in Catch command by using Mathematica

I am using the below command in Mathematica (a example): Catch[Do[i; If[EulerPhi[i] > EulerPhi[i + 1], Print[i]], {i, 1, 100}]] Of course, I would like to do this for other functions (maybe) and for ...
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2answers
21 views

limit of an expression

What is the limit of this expression in terms of some known mathematical constants (if any)? $$\lim_{x\to\infty} \left(\frac{x-1}{x}\right)^x$$
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0answers
52 views

Mathematica legitimacy for research papers

I'm currently working on an undergraduate research project and am close to a paper/poster. A portion of my work involves differentiating a large function, which I did in Mathematica. From there I ...
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0answers
14 views

What is the convergence property of $a_k$ when $a_{k+1} \le c_k a_k + b_k$?

what is the convergence property of $a_k$ when $a_{k+1} \le c_k a_k + b_k$? Here, $c_k < 1$ and $b_k$ are decreasing functions of $k$.
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3answers
50 views

plotting a function i

How can i plot bellow function in MAPLE or MATHEMATICA or MATLAB? $$y=0.05+0.1\cdot e^{0.01x}\cdot \cos(0.2\cdot x)$$ while $x$ can be in the range of $ -350$ to $+350$ or less. Thank you
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1answer
22 views

Finding subsets with a certain constraint with Mathematica

I would like to write some Mathematica code to find all the subsets of $\{1,2,\ldots,n\}$ subject to the constraint that there should be exactly one pair of consecutive integers in each subset. So for ...
1
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1answer
46 views

Deriving the BBP identify for $\pi$

I was given a problem to learn how to use Mathematica. I should derive the identity from the paper 1 known as the BBP formula for $\pi$. But I can't figure it out why $$\begin{equation} \sum_{k=0}^{\...
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1answer
38 views

Show a matrix is a linear transformations [closed]

So I know I need to multiply my transformations by (1,0) and (0,1) but I’m unsure how to get the transformations as if I multiply just by the given matrix I get the same answer please help.
2
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0answers
33 views

derivation of limit not given in workbook $\lim_{m \to \infty}\frac{\mu_m}{m}$

Let $\mu_m=\sum_{k=0}^{\left \lceil{m/2}\right \rceil }k\frac{{m-k+1}\choose k}{f_{m+2}}$ where $f_{m+2}$ is the $m+2$th Fibonacci number with $f_1=f_2=1$. Then $\lim_{m\to\infty}\frac{\mu_m}{m}=(5-\...
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0answers
17 views

The meaning of this please $\in \mathbb{Z}_{10}$ ( with small 10)?

I need to know if it's the right meaning of this expression please : $\in \mathbb{Z}_{10}$ ( Z with 10 in the bottom): integer numbers / whole integer numbers set (with ten ). Can you please ...
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0answers
17 views

What is the kernel of a linear recurrence?

There is the Mathematica command: $$ \texttt{LinearRecurrence[ker,init,n]: gives the sequence of length n}\\ \texttt{obtained by iterating the linear recurrence with kernel ker}\\ \texttt{starting ...
2
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1answer
40 views

How to define a function with subscripted variable in Mathematica?

How to define a function with subscripted variable? I want to write the following expression $$f[a_9] =1+ a_7 + a_9$$ I tried to write "f[Subscript[a, 9]_ ] := 1+ [Subscript[a, 7]+ [Subscript[a, 9]" ...
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1answer
62 views

Software which writes long math expressions in short form by detecting the patterns?

Is there any software which can detects the patterns in long math expression and collects them as sums and products in short form. I am working with some long expressions of the following forms. I ...

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