New answers tagged

2 votes

Symbolic scalar-by-matrix derivative

Outline Discussion Using Differentials Using the NonCommutativeMultiply package NCAlgebra Using MatrixD Using xAct Discussion (code sections below) There is an ambiguity that has not been mentioned. ...
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2 votes

Modify derivative expressions with substitutions

OK...I think I got it, but maybe not the most efficient way. Need to add a conditional /; dy-1 >= 0 before the rule ...
3 votes
Accepted

Derivative of piecewise function returns one more case

Clear["Global`*"] Instead of using g != 1 use g < 1 || g > 1, then ...
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2 votes

Derivative of piecewise function returns one more case

It looks like Mathematica insists on having a default condition (with value zero, unless otherwise specifed). With ass=D[U[c,n,g,p],c] You can construct something ...
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7 votes

Symbolic integration and numerical integration yield very different results

The problem is not Integrate, but the numerical evaluation following Integrate. Consider for example ...
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2 votes

Mathematica doesn't evaluate an expression

I think your expression E[t] inside Solve should be Exp[t]. Try this instead, where I ...
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4 votes

Definite Integration by parts

There's a resource function, based on the the internal utility ResourceFunctionHelpers`IntegrateByParts: ...
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3 votes
Accepted

Evaluate Tricky Multivariable Integral

I solved the issue and thought it instructive to post the solution: A contributor in the comments mentioned using NumericQ with ...
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6 votes
Accepted

How to calculate this integral with highly oscillating integrand?

Here's a fast way: ...
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4 votes

How to calculate this integral with highly oscillating integrand?

Stripping "GlobalAdaptive" of the "extras" produces correct results quickly: ...
4 votes

How to calculate this integral with highly oscillating integrand?

The issue with this integrand seems to be the highly oscillatory nature which makes it difficult to find the right step spacing. In the following I will give two methods to deal with the small step ...
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4 votes

How to calculate this integral with highly oscillating integrand?

With patience, Monte Carlo methods can be effective ...
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3 votes

How to calculate this integral with highly oscillating integrand?

It's kind of a pain, but you can break up the integral yourself. integrand = (Cos[2022*t]*Sin[10050*t]*Sin[10251*t])/(Sin[50*t]*Sin[51*t]) To determine where one ...
  • 7,584
4 votes

Can this type of function be plotted faster using NDSolve instead of NIntegrate?

Note: This is an extended comment. This integral can be expressed in terms of the MeijerG special function: ...
  • 7,468
6 votes

Can this type of function be plotted faster using NDSolve instead of NIntegrate?

How can I apply NDSolve to this function? Do you want to apply NDSolve or do you want to plot the integral faster? The plot can ...
7 votes

How to calculate this integral with highly oscillating integrand?

Note: As OP has pointed out in a comment, a similar calculation is available here on Math SE. OPs integral can be written as $$ \int_0^{2\pi} f(50t) f(51t) \cos(2022 t) dt $$ with the auxiliary ...
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9 votes
Accepted

Consecutive neighbours of Hypergeometric ${}_1 F_1(a,b,z)$

For $c\approx0$ we can use a series-expansion for the second term on the right-hand side: $$ _1F_1(a,c;z) = \frac{a z}{c}{_1}F_1(a+1,2;z)+O(1) $$ which turns the OP's expression into an approximation ...
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4 votes
Accepted

General limit of a function with Pochhammer for any natural number

The function can also be written as f1[z]*f2 where ...
  • 7,468
1 vote

Need help with Assumptions for an integral

...
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3 votes

Plot eigenvalues of fractional Laplacian in 1D

We can compute eigenvalues with using Haar wavelets collocation method as follows (see also our code here) ...
  • 35.3k
1 vote

How could I deal with and mark point of singularity or non-existance?

Dibbo: Best if you break it up into small parts and test them separately. First just need to get the DE working. You have three bugs: You define b=2 but specify it as a parameter in ...
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1 vote

I'm trying to solve the indefinite integral of a real function (with a bunch of real parameters inside) but the result is a complex function

the result is a complex function and I cannot accept this solution. Maple 2022.1 gives anti-derivative with no explicit I in it. Here it is. It is in terms of cos/...
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0 votes
Accepted

How to plot several lists for different values of independent variable in a same graph?

We can use Do loop as follows ...
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3 votes
Accepted

Possibly incorrect result of DiscreteLimit

In version 13.1 on Windows 10 ...
5 votes
Accepted

Integrate[Sqrt[(1 - Cos[t])/(Cos[a] - Cos[t])], {t, a, Pi}, Assumptions -> 0 < a < Pi] gives a Complex Expression rather than Pi

Assumptions are not always applied as constraints. (Took a bit extra massaging to get the result of Integrate into its fully simplified form under the assumptions.) ...
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4 votes

Integrate[Sqrt[(1 - Cos[t])/(Cos[a] - Cos[t])], {t, a, Pi}, Assumptions -> 0 < a < Pi] gives a Complex Expression rather than Pi

$a$ needs to be between 0 and Pi/2 so that Cos[a] remain positive in order to simplify the sqrt which comes into play using the ...
  • 116k
1 vote

How to solve ODE Bernoulli type equation plus a constant?

Actually the ode $\frac{dx}{dt}=a x- b x^c$ is not Bernoulli. It is simply separable since $a,b$ are constants. The same with $\frac{dx}{dt}=a x- b x^c+d$ is separable. Bernoulli has the form $\frac{...
  • 116k
1 vote

How to plot existance of solution vs non-existance for the following ode?

want to see or devide the region for solution of existance vs non-existance. You could use ParametricPlot3D to see the solution as you change the parameters? But ...
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2 votes
Accepted

Limit of hypergeometric series and gamma function

Use this identity from the Wolfram functions website. This reads: ...
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3 votes

Limit of hypergeometric series and gamma function

Here is a solution with a bit of manual work. Note that HypergeometricPFQRegularized is close to what OP wants. So define ...
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4 votes
Accepted

Unable to solve the given equation

Replace your last line with this and it finishes in few seconds Block[{δ1 = 0}, Solve[Simplify[Veff'[r] == 0], r, Reals]]
  • 116k
1 vote

Integrating $\int \frac{z-z'}{\left(x'^2+y'^2+(z-z')^2\right)^{3/2}}dV$

This is an extended comment. I will consider a related problem in 2 dimensions using integration over a Ball of radius 1. I understand what the correct solution is (...
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8 votes
Accepted

Integrating $\int \frac{z-z'}{\left(x'^2+y'^2+(z-z')^2\right)^{3/2}}dV$

It helps to guide the integration, in the same way as it would be done manually. Convert to spherical coordinates: ...
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5 votes
Accepted

How to develop a particular solution for inhomogeneous ODE using an Ansatz method and variation of parameters

But how do I plug them in the code above? I do not know how to explain this in words in comment section other than by showing it. The $y_p$ is found using variation of parameters by applying the ...
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2 votes
Accepted

Bug in FullSimplify

I'm not sure this is truly a workaround, since your original Sum will not yield a function of x, but for this particular case we can notice that ...
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1 vote

Plot of massless particles on unstable null circular geodesic : Finding an alternative for Graphics`Mesh`FindIntersections and reducing code length

This is a more functional way to do step 1: ...
4 votes
Accepted

Plot The Magnetization

Function g[k_] := Tr[Eigenvalues[h[k]]] is periodic with a period of 4 Pi, therefore we suppose that integral should be defined ...
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2 votes

This trigonometric integral "has exceeded the time limit for your plan"

TrigFactor and TrigReduce the integrand to see a systematic, FourierCos like expansion depending on n. ...
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3 votes

This trigonometric integral "has exceeded the time limit for your plan"

Somehow trig integrals, especially those with parameters and removable discontinuities, often have tricky antiderivatives. One can apply a standard identity: ...
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2 votes

This trigonometric integral "has exceeded the time limit for your plan"

In 13.1 on Windows 10 Integrate[Sin[(2 n + 1) x]/Sin[x],{x, 0, Pi/2},Assumptions -> n \[Element] PositiveIntegers] Pi/2 ...
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8 votes
Accepted

This trigonometric integral "has exceeded the time limit for your plan"

One alternative: Table[Integrate[Sin[(2 n + 1) x]/Sin[x], {x, 0, Pi/2}], {n, 0, 10}]
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1 vote
Accepted

Trouble with output of Reduce as a root object for a 3d Plot

...
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5 votes

Approximating surface with tangent planes

Thanks @Michael E2 point out that quadratic paraboloid work. Here we use the definiton of differential of function to get the tangent plane for 2-variables function,see ...
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