Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of Wolfram Alpha.

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41 views

Why Mathematica doesn't evaluate the derivative of the logarithm? [closed]

I'm trying to compute the second-order derivatives of the negative log likelihood as follows: $$ P(t) = \int_{0}^{t}p(v)dv\\ \mathcal{L}(t)=-\eta_n\log\left(1-P(t)\right)\\ $$ Where $P(t)$ is the CDF ...
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2answers
26 views

Is there a way to plot separate functions in 3D using Wolfram Alpha?

Is there a way to plot separate functions in 3D using Wolfram Alpha? Am I doing something wrong? Similar problem with GeoGebra
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2answers
37 views

Why are $e^{-4\ln(-x)+4}$ and $e^{-4\ln(-x)}$ positive?

Algebraically, why is $e^{-4\ln(-x)+4}$ a positive result but $e^{-4\ln(-x)}$ a positive result? It seems like with logarithmic properties, they should both be negative, but Wolfram Alpha shows the ...
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1answer
29 views

Software for evaluating summation expressions involving Stirling numbers of the first kind.

I know that for a summation such as $$p=\sum_{n=o}^{k}{\binom{k}{n}}=2^k,$$ Wolfram Alpha and some other computational software can easily tell that indeed the above summation evaluates to $2^k$. I ...
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1answer
24 views

Matrix representation after change of basis

I am trying to solve this task using Wolfram Notebook. I would like to know how new matrix is calculated (part b) after a change of basis. Part a: I decided to show this part because part b is a ...
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1answer
34 views

Solving a seemingly-trivial trigonometric equation for a specific variable

I'd like to express $y$ in $y = \sin (x*y)$. I can get $x = \frac{\arcsin y} y $ without any issues and then kind of don't know how to continue. WolframAlpha seems to have struggles with the equation ...
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2answers
44 views

Wolfram: doing substitution on indexed terms

I have sx = Sum[Indexed[x, i], {i, 1, 10}]^2 // Expand It expands in sum of 55 terms, from which $x_i^2$ - 10 terms, actual representation: $x_1^2+x_2^2+x_3^2+...$...
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2answers
40 views

Equivalent forms for $\int \csc(x) dx$

This question asked about two common forms commonly given for $\int \csc(x) dx$, specifically: $$ (1) \qquad \int \csc(x) dx = \mathbf{{\color{red}-} \ ln|csc(x)+cot(x)| + C}, $$ and $$ (2) \qquad \...
3
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2answers
132 views

Shouldn't the ith root of the complex exponential function be equal to the natural exponential function?

When i plug $\sqrt[i]{e^{ix}}$ into WolframAlpha it shows a rather weird function considering it should show the natural exponential function, since $\sqrt[i]{e^{ix}}=(e^{ix})^{\frac{1}{i}}=e^{\frac{...
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2answers
47 views

What are $c$'s in antiderivative of double integral in Wolfram Alpha

I would like to solve the following double integral: $$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} (x y)^{-\theta - 1} dx \hspace{1mm} dy$$ Using Wolfram Alpha for symbolic algebra, it gives a ...
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1answer
45 views

Wolfram Alpha: How to solve a system of linear equations with variable terms

I'm trying to use Wolfram Alpha to solve the following system of equations (for $x, y$; given $ad - bc \neq 0$) in order to confirm that I solved it correctly by hand: $$ ax + by = 3 \\ cx + dy = -4 $$...
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0answers
26 views

Derivative of this complex function

Assume that I have the following complex function $$f(Z)=\frac{1}{2\pi i}\left(-0.5a(Z-1)\ln \left( \frac{Z-1}{Z+1} \right) +0.5b(Z+1)\ln \left( \frac{Z-1}{Z+1} \right) \right)$$ where $Z$ is some ...
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0answers
26 views

Calculating daily sunlight hours on the North side of a hill with Wolfram Alpha

I recently bought a house that sits on the North side of a hill. The owners say that for a couple of days out of the year the sun never rises over the hill. It got me thinking of using Wolfram Alpha ...
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0answers
85 views

WolframAlpha and the sum $\sum_{k=1}^{n}\frac{\cos(\pi k)}{\csc(\pi k)}$

Question: WolframAlpha gives the following expression $$\sum_{k=1}^{n}\frac{\cos(\pi k)}{\csc(\pi k)}=\phi(n);$$ where $\phi()$ is the Euler totient function. You can check for yourself here. Is this ...
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2answers
57 views

Wolfram Alpha is giving two different results for the same computation - why?

I'm exploring the convolution of a rectangle function scaled by a factor of $\displaystyle{n}$ with a Gaussian function/standard normal distribution of varying parameters (example 1, 2, 3) using ...
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2answers
91 views

Steps for solution of $\frac{dy}{dx}-y^2=\frac{a}{x}+b$ [closed]

According to Wolfram, $$\frac{dy}{dx}-y^2=\frac{b}{x}+a$$ The equation above has the solution; Where $a$ and $b$ are constants. $_1F_1(a;b;x)$ and $U(a,b,x)$ are the Kummer confluent hypergeometric ...
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4answers
68 views

How to get WolframAlpha to determine $f(2)$ when $f(x)=3x^2-2x+\int_0^2f(t)dt$ [closed]

This is my first question at StackExchange. It's about WolframAlpha. The function $f(x)$ is defined as: $$f(x)=3x^2-2x+\int_0^2f(t)dt$$ And I'm trying to find the value of $f(2)$. So at WolframAlpha, ...
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1answer
34 views

Addition of a number and a vector

Does it mathematically make sense for a number to be added to a vector (or matrix for that matter)? When I put $4 + [1, 2, 3]$ into Wolfram Alpha it gives me $[5, 6, 7]$, i.e. the number is added to ...
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1answer
39 views

Software to solve equation

I'm trying to solve the following equation: \begin{align} 100.474 &= \frac{1\cdot 1000}{\left(1+18.94833392\right)} +\frac{1\cdot 1000}{\left(1+5.3028 \right)^ 2}+\\ &\frac{1000\cdot 1}{\...
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1answer
33 views

Global minimum for $\frac{2(q - 1)(q^k + 1)}{q^{k+1} + q - 1}$, if $q \geq 5$ and $k \geq 1$

Let $q$ be a prime number, and let $k$ be an integer. THE PROBLEM Does the function $$f(q,k) = \frac{2(q - 1)(q^k + 1)}{q^{k+1} + q - 1}$$ have a global minimum, if $q \geq 5$ and $k \geq 1$? MY ...
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1answer
47 views

Integral of a product of Bessel functions of the first kind

I want to do this integral $H(\rho)=\int_{0}^{\infty} J_1(2 \pi Lr)J_0(2\pi \rho r)dr$, where $J_1$ and $J_0$ are Bessel functions of the first kind and $L\in \mathbb{R}$ is a constant, so I tried to ...
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1answer
111 views

Why can't Wolfram Alpha calculate $\int_0^{2\pi}\sqrt{(a-\cos\theta)^2+\sin^2\theta}\ d\theta$?

In this answer to How is the average distance between 2 objects orbiting around a third object calculated? I had to integrate $$\int_0^{2 \pi}\sqrt{(a-\cos \theta)^2 + \sin^2 \theta} \ d\theta.$$ I ...
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0answers
23 views

Closed form of a series similar to exponential [duplicate]

I do not know if the question has already been posted. I was trying to find a closed form for the sum $$ \sum_{n=0}^{\infty}\frac{n^x}{n!} $$ Is there a special function to think about (polylogarithm.....
2
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1answer
81 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
42 views

Triple series with WolframAlpha where the series are interdependent

How can be written a triple series with WolframAlpha where the series are interdependent like, for instance, the following ones? $$\sum_{i=1}^{n-2} \sum_{j=i+1}^{n-1} \sum_{k=j+1}^{n} \min\{j-i,k-j\}~....
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1answer
35 views

Double series with WolframAlpha where the series are interdependent

How can be written a double series with WolframAlpha where the series are interdependent like, for instance, the following ones? $$\sum_{j=1}^i \sum_{i=2}^n (i^2-j)$$ (I don't get, as expected, a ...
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1answer
65 views

What's going on with this Wolfram Alpha matrix multiplication?

I was computing the matrix exponential of $$X = \begin{pmatrix} 1 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 1 \end{pmatrix}$$ by diagonalization. Wolfram Alpha and Symbolab both ...
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0answers
25 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
61 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
26 views

Wolfram Alpha for Integer Programming

I am new to Wolfram Alpha. The following command gives me real number solutions: max 8*p+20*q, p+q ≤11, 3*p+2*q≤30, p+3*q≤28, p≥0, q≥0 The solution is p = 5/2 and ...
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0answers
16 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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0answers
21 views

how to use implicit differentiation using Wolfram alpha. two dependent variables

Im stuck trying to feed the formula into Wolfram alpha, I gotta solve for $\frac{d}{dt}{x^2y^2}=16$
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1answer
60 views

I found an unusual (at least for me) answer in Wolfram Alpha I don't understand

Sorry in advance, is my first question and i found something weird in wolfram The problem: Given a function f, and a chain of links with lengths (h0, h1, h2...), calculate the points where every ...
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1answer
83 views

Should I waste my time with wolfram alpha to solve such problem like $x^3+y^3+z^3=390$?

I'm sorry to ask this question probably it is not suitable here. However I read some papers in number theory related to the solution of $x^3+y^3+z^3=n$ for some known solved problem about ...
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1answer
29 views

Specify parameters Wolfram Alpha

Hopefully, this kind of question is ok, have seen a couple of other WA-queries that hasn't been downvoted. Apologies if not. I want to minimize say $f(x)=ax^2+bx+c$. Wolfram Alpha gives me an ...
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3answers
70 views

How do I calculate the sine integral for a specific input?

I need to solve an equation containing the Sine Integral $\mathrm{Si}\left(\frac{2 k \pi}{x}\right)$ in mathjs which doesn't have the $\mathrm{Si}$ function. Is there another way to represent this? ...
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1answer
22 views

Series expression by using Puiseux series

I wanna express this series $$\sqrt{1}+\sqrt{2}+\sqrt{3}+\sqrt{4}+...+\sqrt{n}$$ as Puiseux series. According to "Wolfram Alpha", it says $$\frac{2n^{3/2}}{3}+\frac{\sqrt{n}}{2}+\zeta(-\frac{1}{2})+\...
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0answers
81 views

What are the mathematical steps used to get this $42=(-80538738812075974)³ + 80435758145817515³ + 12602123297335631³$?

I have accrossed this representation in cubic sum $42=(-80538738812075974)³ + 80435758145817515³ + 12602123297335631³$ at this website but am confused how mathematicains proved this , Now Is this ...
1
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1answer
84 views

Why does $\tan\left(\frac{1}{x}\right)$ look different to what I expect it should look like on WolframAlpha as x approaches 0?

https://www.wolframalpha.com/input/?i=tan%281%2Fx%29%2C+-0.01+%3C+x+%3C+0.01 $$$$ https://www.wolframalpha.com/input/?i=tan%281%2Fx%29%2C+-0.001+%3C+x+%3C+0.001 $$$$ For larger intervals of x, ...
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3answers
65 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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1answer
52 views

Is it mathematically valid to take the limit of an **equation** as opposed to an expression?

Wolfram Alpha seems to think it's okay to write this: $$\lim_{n \to \infty} (n=\frac{n^2}{n})=True$$ I understand what is meant, and also why it returns True, but is this a mathematically valid ...
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1answer
57 views

Wolfram Alpha is doing something I don't understand, please help

I am using Newton Raphson method to obtain the velocity of a chemical reaction, and I needed to derive the next equation:$$\frac{d}{dk}\left(\left(\frac{0.35}{k}\right)^{\frac{k}{k-0.35}}\right)= -0....
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2answers
59 views

Find $a, b, c$ such that element $x=a\alpha^2+b\alpha+c \in \mathbb{Q}[x]/\langle x^3+x+11 \rangle$

I'm trying to generate a fundamental unit of the number field $K=\mathbb{Q}(\alpha)$, where $\alpha^3+\alpha+11$. I found a non-trivial unit and I need to find $a,b,c\in\Bbb{Q}$ such that $$\frac{(-...
2
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1answer
90 views

Help with gnarly integral from fluid mechanics

I'm working on a 2D fluid simulator and a particularly gnarly integral came up. First, I have two functions in polar coordinates which look like: $$F(\theta) = cos(2\theta+\psi)$$ $$ G(\theta) = \...
0
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1answer
58 views

What is this method of solving called and why does it work? (From WA)

Wolfram Alpha uses a scary-looking algebraic method to solve $x^{3}-x-1=0$ that I've never encountered before. It seems that every other online algebra calculator uses numerical methods, such as the ...
0
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3answers
539 views

Computer tools to solve linear system of equations with singular matrix

According to the theory I've read, if $A$ is singular, the equation $A\vec{x}=\vec{b}$ will have either zero or infinitely many solutions. I tried solving this equation for: $$A=\begin{bmatrix} 4 &...
0
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2answers
44 views

Find the leading digit(s) of a factorial

What are the better methods (algorithms) to computing the first number (or few leading numbers) of a large factorial. Wolfram alpha seems pretty fast and handles large numbers. Is it accurate? Does ...
0
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0answers
89 views

How to calculate the area of a polar curve in Wolfram Alpha?

I know I can use plot polar r = cos(3theta), theta from pi/6 to -pi/6 to plot the polar curve of a equation, but I would like to check if my math is correct when calculating the area inside the curve. ...
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4answers
129 views

How to plot the polar equation theta = pi/6 on wolframalpha

I need to plot the polar equation theta = pi/6 My question has two parts. 1) Is it a line? I'm pretty sure it is, since the angle theta in the polar equation is a constant, but since I was not ...
0
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1answer
41 views

intersection of numbers on wolfram [closed]

After evaluations of the Riemann Hypothesis, with reflective thoughts over a year as to how to solve it, a formula that is very close has been found, if not distinctly the act of the original proof, ...

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