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Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of Wolfram Alpha.

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1answer
90 views

Wolfram alpha solve differential equation assume real positive parameters

I'm trying to solve the following differential equation with Wolfram Alpha (I have a pro subscription): y''+2*a*y'+(a^2-c^2-b/d*Exp(-x/d)-b^2*Exp(-2*x/d))*y=0 I ...
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2answers
57 views

Understanding this graph

The function is given as $f(x)=2x+3x^\left(2/3\right)$. The enclosed graph is from wolfram.. My question is why doesn't $f(-1)=1$ show up to the left of the y axis. I don't see why the domain of ...
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0answers
14 views

Using WolframAlpha to check cycle products for figuring out L/R cosets

I've been told and have noticed that WolframAlpha computes the order of elements a little differently than my class. How would I plug in multiple cycles so that I can check my work? I have noticed ...
27
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4answers
6k views

Why does Wolfram|Alpha make a mistake here?

We want to evaluate $$\lim_{x \to -8}\frac{\sqrt{1-x}-3}{2+\sqrt[3]{x}}.$$The solving process can be written as follows:\begin{align*}\lim_{x \to -8}\frac{\sqrt{1-x}-3}{2+\sqrt[3]{x}}&=\lim_{x \to ...
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4answers
56 views

A specific homogeneous polar differential equation

In an assignment of our school, we are asked to solve $$\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{x + y - 3}{x - y - 1}$$ by turning it into a homogeneous polar differential equation (equation of the ...
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0answers
22 views

Reduction of appearing dilogarithms

I have a series of dilogarithms with various arguments and I was just wondering if it is possible to tell if they are all independent (that is to say, cannot be transformed into each other through e.g ...
2
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1answer
54 views

How does this infinite product work?

${\displaystyle \prod_{n=1}^{\infty} ({ \frac n {n+1}}) ^{(-1)^n}}$ Typed this infinite product into Wolfram Alpha and I got an approximate result of 1.5708. I wonder if anyone studied this infinite ...
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1answer
28 views

Wolfram|Alpha: Calculate an expression for $x^2y=-2$

I would like to calculate the expression $(xy)^8*x^8$ knowing that $x^2y=-2$. What should I write in Wolfram Alpha to get the expected result? Kind regards, Alexis.
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2answers
96 views

When does WolframAlpha refuse to give the precise value?

I was computing the length of the curve $y=e^x$ between $x=1$ and $x=2$. When I input "arc length of e^x between 1 and 2" into WolframAlpha, it gives me only an approximation as follows: However, ...
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0answers
31 views

How to perform constraint optimization with undefined parameters in WolframAlpha?

I'm having trouble finding how to do a constraint optimization with undefined parameters in WolframAlpha. For example, how do I solve a standard Cobb Douglas problem such as: maximize $A x^a y^b$ on $...
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1answer
46 views

Relation between dilogarithm and its complex conjugate

I am looking for a relation between the dilog and its complex conjugate, that is can I simplify the following summation of terms $$f(z) = \text{Li}_2(z) + (\text{Li}_2(z))^*?$$ I have looked through ...
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1answer
91 views

Wolfram Alpha Ignoring Log Rules?

Why does Wolfram Alpha say that $\underbrace{\ln(y(y^{2}-4))}_\text{EQ1} \neq \underbrace{\ln(y) + \ln(y-2) + \ln(y+2)}_\text{EQ2}$ (seen here)? The Produce Rule of Logarithms states that: $$\log_b{(...
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0answers
36 views

How can I get solution to this partial differential equation using Wolfram Alpha?

Solve: $\frac{\partial ^3z}{\partial x^3}-4\frac{\partial^3z}{\partial x ^2\partial y}+\frac{\partial ^3 z}{\partial x \partial y^2}-2\frac{\partial^3z}{\partial y^3}=e^{2x+y} $ I want to get the ...
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1answer
120 views

How to write the index number in the Wolfram Alpha search engine

I am trying to see some results for my sequence in Wolfram Alpha, but I don't know how to enter the "n" letter as an index. My sequence is a_(n+1) = ((3a_n)+2)/5. The reddit answer with underscores ...
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2answers
162 views

Multidimensional chain rule, online calculator

I would like to check my solutions for the derivative with the multidimensional chain rule, and I would like to do that online with a calculator. But I can not find one and I do not know how to use ...
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1answer
70 views

What is the exact value of this : $5\int_{0}^{\infty}\exp(-x^2 \text{erf}(x))x^{\sin x+\frac12}dx$?

My curiousity is to get more integrals about the constant $\pi$ using special functions. I have used some special functions as shown below in the integral: $$5\int_{0}^{\infty}\exp\left(-x^2 \text{...
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3answers
137 views

How to finds primes $p$ with the property that both $10p^2+9$ and $8p^2-9$ are also primes using Wolfram Alpha? [closed]

I want to know the number of primes $p$ that satisfies the condition that $10p^2 + 9$ and $8p^2 - 9$ are both primes, for primes $p$ only. How can I do it using Wolfram Alpha (or any other ...
1
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2answers
88 views

Integral of $(1-x^a)^\frac{1}{a}$

Does the integral $$\int (1-x^a)^\frac{1}{a} dx$$ have a closed form solution? The parameter $a$ is a constant and both $a$ and $x$ are positive real numbers less than or equal to $1$. I tried ...
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0answers
19 views

Approximation for fractional function for given boundary conditions

I try to find an approximation for the following expression $$\tan\phi(x)=\frac{\mathrm{si}(x)\sin(kx)-\mathrm{si}(x-\tau)\sin(k(x-\tau))}{\mathrm{si}(x)\cos(kx)-\mathrm{si}(x-\tau)\cos(k(x-\tau))} \...
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1answer
500 views

Mathematical Explanation of Mathematica Summation ${\sum_{n=1}^{\infty}\frac{(2n-1)!}{(2n+2)!}\zeta(2n)}$

From a mathematical point of view, what phenomena that most likely Mathematica Wolfram encountered when calculating: $$ \sum_{n=1}^{\infty}\frac{(2n-1)!}{(2n+2)!}\zeta(2n)\,=\,\color{red}{\frac{2\...
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1answer
36 views

WolframAlpha, Solve for specific values of Z

Question I have the following command I am entering: solve[y=prime(x-1)+(z)/prime(x-1)+1, z=28] over the integers I would like to be able to say: Solve for z=28,...
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1answer
208 views

Wolfram Alpha - limiting the input X set to prime integer numbers

I was curious if I can get wolfram alpha to calculate for me the values of Y, but using only the prime integer values of X . Currently I have the following: ...
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4answers
90 views

Solution of trigonometric equation avoiding the undefined case

I'm given this trigonometric equation, $$\tan x+\tan 2x=1-\tan x\tan 2x$$ I rewrote it as $$\dfrac{\tan x+\tan 2x}{1-\tan x\cdot\tan 2x}=1$$ Using the identity, $$\tan (A+B)=\dfrac{\tan A+\tan B}{1-\...
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1answer
61 views

How can I plot the following function in wolfram alpha? [closed]

z=x/100 if{(x<100) and y<10000} = 1 otherwise... I dont know how to plot a conditional function
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1answer
30 views

How to plot a “x and y” inequality function

I'd like to plot the following function : $$(\frac{d}{2}+1)\big\lceil\sqrt{8x+1}\big\rceil \leq 2x(\big\lceil\sqrt{4d+1}\big\rceil-1)+1$$ It's ok to plot without the ceiling function I suppose. So ...
1
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1answer
132 views

How to solve recurrence equation by gamma function?

I have a recurrence equation and I have no idea how to solve it. $$a(n)=(1-\frac{1}{n}+\frac{X}{n})a(n-1)+\frac{2}{n}$$ $$a(1)=1$$ where X is a constant I tried to put it into Wolfram and I got the ...
2
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2answers
40 views

Behavior of :$\sum_{n=k}^{+\infty} n^{-\frac{n}{\log n}}$ with $ k$ is natural number

I'm confused about behavior of this series :$\sum_{n=k}^{+\infty} n^{-\frac{n}{\log n}}$ with $k$ is natural number , for $k=0 ,1$ the series converges according to wolfram alpha assumption ...
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0answers
174 views

How can I restrict a variable to a given domain in Wolfram Alpha?

Ever since I began using Wolfram Alpha for quick online calculations I have had trouble specifying the domain of my variables. Note that I have already read the related MSO question "Tell Wolfram ...
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1answer
89 views

How to estimate the number of roots and their multiplicity in some interval when polynomial has fractional powers?

Let's say you have the polynomial with fractional power: $$P(z)=z^{9/2}-\frac{3}{2} z^4 +\frac{1}{2} z^3=0, \quad z \in \mathbb{C} \tag{1}$$ I have found two real roots of Eq. (1): $$z_1=0,$$ and $$...
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1answer
43 views

Wolfram generating different graphs for equivalent equations

Wolfram generates this funky graph for eˣ = sin(x·y): Whereas for the equivalent arcsin(eˣ)/x = y we get this rather boring ...
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0answers
76 views

How to minimize or maximize a function over a finite field in WolframAlpha?

Is it possible to ask WolframAlpha to minimize or maximize a function with variables in a finite field? Let's take a stupid example: how do I ask WolframAlpha to maximize $x_1+x_2$ with $x_1, x_2\in\...
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2answers
88 views

Can someone walk me through this wolframalpha solution?

Given $$x = (625/50)a-(100/50)$$ $$x = (214/60)b-(110/60)$$ The following integer solution was provided by a wolframalpha widget: $$a = 214n+10$$ $$b = 750n+35$$ $...
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1answer
80 views

How can i solve $\frac{x^2}{a}-\frac{x}{b}-\ln(x)=0$

How can i solve: $$\frac{x^2}{a}-\frac{x}{b}-\ln(x)=0$$ for any pair $(a,b)$? For example, if $a=29$ and $b=7$, wolframalpha gives me: $$x= 0.903969\ldots$$ $$x= 10.6013\ldots$$ but it wont show me ...
6
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0answers
101 views

$\prod_{k=2}^n (k^2 - k)$: is WolframAlpha wrong?

I tried to find the product of $k(k-1)$ from $k=2$ to $n$. The partial product values should be 12 at 3 and 144 at 4. But it's showing the wrong partial product. What went wrong? Screenshot
2
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3answers
230 views

Factorization of a real polynomial

Can I factor univariate polynomials with real coefficients as a product of quadratic trinomials and binomials corresponding to the complex conjugate and real roots using Wolfram Alpha ? E.g., $$x^3-...
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2answers
117 views

How to find the exact value of $\cos(\frac{2\pi}{17})$ with WolframAlpha?

I tried to find the exact value of $\cos(\frac{2\pi}{17})$ with WolframAlpha but only obtained a decimal approximation. Is there any way to find this exact value with WolframAlpha?
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2answers
112 views

Is this really true :$\int_{1}^{n}\frac{dx}{\operatorname{\\erf(x)}}= n -\alpha$ with $\alpha$ is constant and $n >1$?

This is $\int\frac{dx}{\operatorname{\\erf(x)}}$ a simple form integral which i can't to evaluate using variable change and integration by part to get it's form, but some computations in wolfram alpha ...
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1answer
36 views

Contradiction of computation of this:$\lim _{x\to 0^+} (\frac{({2}^{(e^{x^\frac32}+1)}-4)^2}{\sin^6{(\sqrt{x}})})$ with wolfram alpha?

I have claculated :$\lim _{x\to 0^+} (\frac{({2}^{(e^{x^\frac32}+1)}-4)^2}{\sin^6{(\sqrt{x}})})$ I have got $( 4\log 2))^2$ as shown below ,but wolfram alpha assumed it equal $\infty$ , then my ...
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2answers
101 views

What is $\lim_{x\to\infty} \sin x$?

What is $$\lim_{x\to\infty} \sin x$$ ? I always thought it was undefined; however, Wolfram|Alpha says that $$\lim_{x\to\infty} \sin x = -1 \text{ to } 1$$ Now, what is the correct answer? What ...
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1answer
383 views

Can WolframAlpha calculate a multivariable integral over arbitrary domain of integration?

If I had an integral specified like this: $$\int_{0}^{1}dx \int_{2}^{3} dy \int_{y^2+5}^{y-4} xyz \ dz$$ I would use this command in WolframAlpha to calculate it: integrate (xyz) dz dy dx, x=0 to ...
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0answers
164 views

Why WolframAlpha does LU decomposition with pivoting even when it isn't needed?

I want to do LU decomposition with $A$: $ A= \left[ {\begin{array}{cc} 1 & 2 & 3 & 4 \\ -9 & 8 & -15 & 4 \\ 2 & 13 & -21 & 7 \\ 4 & -5 & 5 ...
2
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2answers
129 views

Correct computation of Fourier Coefficient in WolframAlpha

It's a very straightforward problem. I have to compute the Fourier series of $$\frac{3}{5-4\cos(x)}$$ I have done it using residues and I have got the following coefficients: $$c_n = 2 ^{-|n|}$$ ...
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2answers
37 views

On multivariable functions and graphs

The definition of graph from Wikipedia is the following: In mathematics, the graph of a function f is, formally, the set of all ordered pairs $(x, f(x))$, and, in practice, the graphical ...
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0answers
32 views

How does one test whether a positive integer is semiperfect in Wolfram Alpha?

Wolfram Alpha allows to test whether a positive integer $n$ is abundant, deficient or perfect. However, I was not able to find a way to test whether $n$ is semiperfect (i.e., equal to the sum of all ...
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1answer
33 views

How to plot all points that are defined by $(4\kappa+2(\lambda \mod 2), 2\lambda\sqrt 3)$ in Wolfram Alpha?

How to plot all points that are defined by $(4\kappa+2(\lambda\mod2), \ 2\lambda\sqrt 3)$ for some $\kappa$ and $\lambda$ that are integers in Wolfram Alpha? I just want to know what this set of ...
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1answer
94 views

What is this strange notation in the output of Wolfram Alpha?

For some reason I need to find the values of two positive integers $k$ and $x$ such that: $$ k x^3 (2 x + 1)^3>2 (k + 1) (x + 1)^2 (2 x^4 + 2 x^3 + 3 x^2 + 2 x + 1). $$ Inputting this in Wolfram ...
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1answer
38 views

What is meant by `DiracDelta'[t]`?

While calculating an inverse Laplace transform Wolfram Alpha returned to me the following output: ...
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3answers
55 views

How to calculate this sum with binomials?

In this paper An Improved Algorithm for Decentralized Extrema-Finding in Circular Configurations of Processes from 1979, in chapter with analyze of average number of passes messages I found this ...
3
votes
1answer
59 views

What is happening here? [Wolfram]

When I input: $2^{a/b} = (2^a)^{1/b}$ Into Wolfram Alpha, it produces a very strange looking "implicit plot": I'm entirely sure what this means or what it's even trying to plot and how. I suspect ...
2
votes
1answer
250 views

Wolfram Alpha: Simple Arithmetic with named constants replacement

I want to verify an equation I implemented in a computer programming language using WA. For example: $\frac{s^2}{((s+w_0)(s+w_1))}$ And specify values for $s, w_0,$ and $w_1$. I have tried: $\...