All Questions
Tagged with calculus-and-analysis assumptions
144 questions
1
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How to assume "much greater than" when there are multiple assumptions? [closed]
Assume $r_{o1} \gg R_S, r_{o2} \gg R_S, g_{m1} r_{o1} \gg 1, g_{m2} r_{o2} \gg 1$.
$$Z_{out} = \frac{r_{o1} (R_S + r_{o2})} {r_{o2} + R_S (1- g_{m1} g_{m2} r_{o1} r_{o2})}$$
Here is what I tried to ...
- 1,892
1
vote
1
answer
185
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How to compute this integral $\int_{-\frac c2}^{0} e^{-a \left(\frac{b x^3}{2}-\frac{x^2}{4}\right)} dx $? [closed]
I want to compute this integral:
$$ \int_{-\frac c2}^{0} e^{-a \left(\frac{b x^3}{2}-\frac{x^2}{4}\right)}
dx \qquad\textstyle{with}\qquad a,b>0 \qquad\textstyle{and}\qquad a,b\in\mathbb{R}$$
The ...
- 749
3
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1
answer
179
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1
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0
answers
56
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How to assume a function is holomorphic?
For example, for a holomorphic function $f(z)=f(x,y)$, it's well know that $\ln |f|$ is harmonic. I want to check it with mathematica with the following code:
...
- 141
1
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0
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111
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Integral of complex exponential with assumptions
I feel confident this problem has been posed before but alas I cannot find it.
...
- 42.3k
2
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2
answers
113
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Computing a limit with assumptions
This program solves the recurrence for the expected time to extinction of a linear birth and death process with arrival rate A and death rate q A, and then attempts to simplify.
...
- 2,166
2
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1
answer
155
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Evaluation of integral with parameters
I am trying to solve the following integral having two strictly positive parameters:
...
- 23
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1
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50
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Assisting Solve to generate solution to a complicated equation
I have the following Mathematica code:
...
- 2,963
3
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1
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126
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Assume asymptotic value in a limit?
Is it possible to give Mathematica a limit about's function at infinity?
For example I would like to
...
- 790
0
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0
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94
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Why do I get different results for this complex line integral?
I want to compute line integral of $f(z) = \frac{1}{z(z-1)^{n+1}}$ over a closed curve $\gamma: t \mapsto 1 + \frac{1}{2} e^{i t}, t \in [0,2\pi]$ in the complex plane in two different ways but the ...
- 153
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64
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Double variable integration unable to prove that integration limits are real
I have simple question regarding double integrating a function.
J*Integrate[Integrate[Cos[ArcTan[Sqrt[(x - a)^2 + (y - b)^2]/L]], {b, -b, b}], {a, -a,a}]
The error ...
- 23
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1
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66
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Integral behaviour?
I'm trying to find a standard integral, which shows itself up in general relativity (proper distance in Schwarzschild metric). For example in this video. The integral is shown as
where $r_s< r$ ...
- 790
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1
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73
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What is the most efficient/optimal way to simplify the given function? Does the given code need more assumptions?
I have a very long function for $\{x,b\}\in\mathbb{R}$ and $n=\{1,2,3,4,5,6,7,8,9,10\}$; here, I have only mentioned a short part of that. The function is a sum of the complex exponentials (a picture ...
- 1,159
0
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1
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49
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Need help with Assumptions for an integral
I want to solve this Log, Integrate[2a Log[-a+((A0 + (y-y1)²)^½, {y1, 0,b}]
But Mathematica only gives me long conditional expressions or imaginary numbers. I (my thinking which can be wrong) assume I ...
- 1
6
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2
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207
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Making a substitution within a typeset integral
This question derives directly from this one, but concerns instead a different matter... one related to display format.
This integral
$$I = \int\limits_2^4 \frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\...
- 42.3k
2
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2
answers
289
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Why is my integral with the error function not being evaluated?
I'm new to Wolfram Mathematica and I was trying to evaluate this integral in particular:
$$\int_{0}^{x}\frac{e^t \operatorname{erf}(\sqrt{t})\sqrt{\pi t}+1}{\sqrt{\pi t x -\pi t^2}}\mathrm dt$$
The ...
2
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1
answer
161
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Integrate ignoring assumptions
I want to evaluate an integral with all variables real and positive. Specifically,
...
- 399
6
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3
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196
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Extracting a logarithmic divergence of an expression using Series
Consider the following expression:
...
- 1,553
1
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1
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36
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Getting the same result from Integrate as Probability
I'm trying to solve a Baysian inference problem (although the details are not all that important for this question)
I define two probability distributions P and <...
- 829
0
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2
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62
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`Assuming` combined with mathematical notation of `Integrate`
I am trying to write down the following expression
Integrate[Exp[-a/2/x]/x/(x + 1), {x, 0, b}, Assumptions -> a > 0 && b > 0]
using mathematical ...
- 1
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2
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241
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Assumptions in Integration for positive real values [closed]
I want to evaluate the following integral in Mathematica.
$$ \int_0^\infty \frac{a^{-t}-b^{-t}}{t} dt = \ln \left(\frac{\ln b}{\ln a} \right)$$
I try to enter this, but Mathematica can't figure it out....
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3
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1
answer
295
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Mathematica tries to differentiate Abs[x] and this causes a problem? [duplicate]
I am trying to run the following code:
...
- 5,573
2
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1
answer
72
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Identical integral evaluating differently
I am trying to compute an integral but am getting two different answers using two near-identical methods. I wish to know why they differ.
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- 95
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1
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125
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Adding Assumptions in double integral written in "math input" mode
I've the following double integral and I'd like to write Assumptions->Re[c]>0, but if I try to do it, I get a syntax error. How can I add the above condition but without changing the ...
- 959
0
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1
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233
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The derivation and simplification of the functions HeavisideTheta and Dirac
I encounter some problems, can you help me? Thanks.
Step (1) gives the expected result 3 DiracDelta[x], why (2) and (3)
can not give expected result ...
- 693
1
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2
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57
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How to assume some variables to "not" be a function of other variables at the time of defining a function [closed]
I have a function with the following definition:
F[x]=Exp[q*w*x];
I want to take total derivatives of F.
How can I define that q and w are not dependent on x at the ...
- 420
0
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2
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84
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Triple integral: How do I include assumptions and conditions?
I would like to solve the following integral:
$$I=\int_{0}^{a} \int_{0}^{y} \int_{0}^{z} e^{(a-x)^{3}} d x d z d y$$
with the condition that:
$$a>0$$
So I tried to input the equation like below ...
user80691
2
votes
1
answer
100
views
How to generate assumptions automatically for definite integrals？
In Mathematica, a trick to speed up the process of definite integrals is by adding assumptions. For example, the following codes run faster if we add such assumptions:
...
- 2,295
1
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0
answers
65
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Why is this integrand not integrating to a Bessel function? [duplicate]
I know from the identities of Bessel functions that the following is true:
$$
J_{m}\left( x \right) = \frac{ 1 }{ 2 \ \pi \ i^{m} } \int_{0}^{2 \pi} \ d\phi \ e^{i \left( x \cos{\phi} \ - \ m \ \phi \...
- 243
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0
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39
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Assume some expression is false
I need to Reduce a complicated function and I want to exclude some conditions A and B. How do I assume that the expression A is ...
- 123
1
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1
answer
91
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2
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1
answer
129
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Can Limit take limits of unknown functions?
For example, when I input this
f[0] = 0;
Limit[f[x], x -> 0]
, it does not output 0.
Is there a way to get it to output <...
2
votes
1
answer
89
views
Trouble evaluating this definite integral, either directly or with indefinite + limits
I have the function
$$
\Sigma(x) = \frac{\sqrt{R^2-x^2}(\left| R\right| -1)}{\left(R^2-1\right) \left(x^2-1\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{R^2-x^2}}{\sqrt{R^2 \left(1-x^2\right)}}\right)-\...
- 233
3
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1
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122
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Mathematica and its default assumptions
I am a bit surprised that evsluating
Integrate[Exp[I n x],{x, 0, Pi}]
gives
$\qquad \frac{-i(e^{in\pi}-1)}{n}$.
What if $n = 0$? I didn't assume anything about $n$ ...
- 613
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1
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110
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0
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0
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51
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Regarding "Assumptions" under "Integrate"
Sir,
I tried to integrate the following in mathematica
...
- 127
1
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1
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227
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Problem with DiracDelta evaluating to zero
I am having an issue (in Mathematica 11.2.0.0) where the following integral evaluates to zero:
...
- 119
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0
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141
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Rubi/Mathematica gives different values for the same integrand
Consider this integral:
$$
\int_0^\pi d\theta \sin\theta\, {1 \over \gamma^q}\left((1-\gamma^2)^2\sqrt{1 \over 1-\left(1-(1-\gamma^2)^4\right)\cos^2\theta} - 1\right)^q
$$
for $0\leq \gamma < 1$. ...
- 119
1
vote
1
answer
123
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complex number from the integration of a real integrand
Consider this integral:
$$
\int_0^\pi d\theta \sin\theta\, {1 \over \gamma^q}\left((1-\gamma^2)^2\sqrt{1 \over 1-\left(1-(1-\gamma^2)^4\right)\cos^2\theta} - 1\right)^q
$$
for $0\leq \gamma < 1$. ...
- 119
1
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1
answer
80
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Two different Integration results for the same integrand in Mathematica
I want to calculate
$$
\int_0^\pi d\theta\sin\theta\, \left(\sqrt{1 \over 1-\left(1-(1-\gamma^2)^4\right)\cos^2\theta} - 1\right)^q
$$.
For the simplest case of $q=1$ we have
...
- 119
1
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1
answer
87
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3
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1
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121
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Display returned integral containing assumptions with integral sign
From solving the PDE example of the general 1 dim heat equation in Nasser Abbasi's site https://www.12000.org/my_notes/pde_in_CAS/maple_2019_and_mma_12/insu157.htm#x182-1810003.1.1 (his problem No 151)...
- 401
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1
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Is it possible to use an assumption that a parameter is an odd or even number?
I am trying to integrate:
Integrate[(Exp[x]*(x^m)/((Exp[x] + 1)^2)), {x, -Infinity, Infinity}]
I know that for odd m the result is zero. How can I tell ...
- 165
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53
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1
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0
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44
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Why does Mathematica miss some solutions for my integral?
When computing the integral of two orthogonal sine functions
$\qquad \sin(n\,\pi\,x)\,\sin(m\,\pi\,x)$, where $n,\,m$ are integers > 0
Mathematica seems to miss the solution where $n=m$. I don't ...
- 33
2
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2
answers
325
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Definite Integration with Exponental Heaviside Step Funtions
As part of an equation of state calculator that I am working on, I have to handle a virial expansion for the equation of state. As such I have to solve for the virial coefficent, $B(T)$, which is ...
- 131
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0
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49
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Solving an integral using assumptions
I am trying to solve the integral
Integrate[(Sin(theta))/sqrt((r^2) + (s^2) - 2 rs(cos(theta))), {theta, 0, pi}]
with assumptions that ...
- 1
2
votes
1
answer
113
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Analytical integration of a composite Dirac delta
From the well-known properties of the Dirac delta function
$ \delta(f(x)) = \sum_k \frac{\delta(x-x_k)}{|f'(x_k)|}
\qquad x_k = \text{zeros of }f(x) $,
$ \delta(f(x))=0
\qquad \qquad\qquad \text{if ...
- 51
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1
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193
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Why are some of my assumptions ignored?
In my opinion Mathematica should be able to further calculate and simplify the output of G1[...].
...
- 335
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1
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77
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