Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

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14
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0answers
241 views

Why does Mathematica choose branches as it does in this situation?

Consider these integrals: ...
9
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0answers
226 views

Is there a way to teach integrate new solutions?

I have an integral which I can solve, but integrate cannot: ...
8
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0answers
57 views

Finding simplifying substitutions for an integral involving limits and integrand

[The following is based on a William Lowell Putnam Mathematical Competition problem.] Consider the definite integral: $I = \int\limits_2^4 \frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\sqrt{\log ...
7
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0answers
162 views

Suspected bug in Integrate

Bug introduced in 9.0.1 or earlier and persisting through 10.0.2 or later In version 10.0: ...
6
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0answers
169 views

Incorrect evaluation for Thue-Morse signed harmonic series

I would like to evaluate $$s = 1 - \frac{1}{2} - \frac{1}{3} + \frac{1}{4} - \frac{1}{5} + \frac{1}{6}+\frac{1}{7}-\frac{1}{8} - ... + \frac{(-1)^{\textrm{binary digit sum}(n-1)}}{n} + ... $$ where ...
5
votes
0answers
127 views

Wrong Limit in Mathematica 10.0.0

Limit[(Log[(3+Sqrt[5])/2]/(2*Log[(1+Sqrt[5])/2]))^(-1-2*n), n -> Infinity] Mathematica (wrong) output: 0 But this is ...
5
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0answers
72 views

LogisticSigmoid residue bug?

On version 10.0 for arm: Residue[LogisticSigmoid[z],{z,I Pi}] gives 0 not 1. Can anyone reproduce this?
5
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0answers
95 views

Integral formula for the inverse Laplace transform doesn't work?

The direct implementation of the definition of the inverse Laplace transform using Integrate fails in the following case: ...
5
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0answers
129 views

Contour Integration along a contour containing two branch points

I need to compute following contour integrations: $$f(u)=\oint_\alpha dz \sqrt{z^3+z+u} \qquad ; \qquad g(u)=\oint_\beta dz \sqrt{z^3+z+u}$$ In which $\alpha$ and $\beta$ are two contours in ...
5
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131 views

Why don't products of Dirac deltas integrate correctly?

The integral $\int \int \ \delta(x) \delta(y) \ dx dy=1$ evaluates to 0 in Mathematica ...
5
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0answers
209 views

Integrate wrong for absolute value of trig function

I was trying to get $\int_0^1 \lvert \cos(2 \pi k x) \rvert \,\mathrm{d}x$ for $k \in \mathbb{Z}$, and was surprised by the result (using Mathematica 10.0.1.0): ...
5
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0answers
203 views

Strange behaviour of MMA in derivatives of some standard functions

There are some peculiar things to be discovered in derivatives of some standard functions in MMA: Strange behaviour Example 1: Abs We have ...
5
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0answers
106 views

Convoluting inverse square root with Gaussian

I would like to convolute the inverse square root on the interval [0,inf] with a Gaussian function, like so: ...
5
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0answers
179 views

Strange Integrate behavior (a bug!)

The following two calculations should give the same result. After all, integration is a linear operation. I have pasted the code below in case you want to play with it. ...
5
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0answers
131 views

Calculating a limit with a result that is discontinuous in the parameters

The following limit is left unevaluated (Edit: added the assumption that $\epsilon$ is real thanks to the comment below): ...
4
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0answers
92 views

Symbolic integration of elliptic functions

Is there some clever way to integrate products of elliptic functions $\wp(z;g_2,g_3)$ or $\zeta(z;g_2,g_3)$ in Mathematica? Mathematica seems to be able to integrate functions like ...
4
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0answers
202 views

Strange result from evaluating a Limit expression

When I evaluate the limit of (1-Cos[x]) Sin[1/x] at x = 0 in Mathematica 9, I obtained ...
4
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0answers
150 views

Version 8.0 integrates but Version 9.0.1 doesn't

I am trying to run the following integral in version 9.0, but it fails: ...
3
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0answers
42 views

Indeterminate expression 0(I*Infinity]) on indefinite integrals on first use only

I do not know if this is new or not, I googled before. Windows 7, 10.1 64 bit: Integrals generate this error message The strange thing also is that the message shows up the first time the command ...
3
votes
0answers
86 views

DiracDelta and version 10.0.0

Note: This issue seems to affect version 10.0.0 only and is fixed in 10.0.1, 10.0.2, and 10.1 When evaluating the following two inputs: ...
3
votes
0answers
66 views

Integrate yields complex value, while after variable transformation the result is real. Bug?

I have the follwoing integral: Integrate[1/Sqrt[0.7 + 0.3*(1 + z)^3], {z, 0, Infinity}, Assumptions -> z \[Element] Reals] >> -3.36354 - 3.85013 I the ...
3
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0answers
96 views

Derivative of generating function (Example from documentation)

In the documentation for GeneratingFunction, the following example is given under Examples -> Properties & Relations -> Derivative: ...
3
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0answers
169 views

Is this result wrong because of calculation time? (and more questions about Assumptions)

I am confused with the Integrate Given by Mathematica. First let's see a one-dimensional case: ...
3
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0answers
154 views

A triple sum related question

I'm trying to compute the triple sum Sum[1/(i! j! k! ), {i, 1, Infinity}, {j, i + 1, Infinity}, {k, j + 1, Infinity}] but Mathematica doesn't return any value. ...
3
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0answers
236 views

Numerical-Symbolical Integration (Calculus)

I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals. The problem with my function is ...
2
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0answers
75 views

Converting integral equations to differential equations

I am trying to use Mathematica to convert integrals to differential equations, of any order. An example of an integral equation is given below, in Mathematica code. Could you please advise as to the ...
2
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0answers
43 views

Computing an inexact derivative with some terms preserved in exact form

I am beginning to learn Mathematica and have the following question: How can I return a derivative with exact numbers instead of one involving numerical approximations? My original, single variable ...
2
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0answers
44 views

Does DynamicModule cure Problem with Manipulate?

Hopefully, this is a final cure for the Problem with Manipulate introduced on A problem with Manipulate and then continued on Continuation of a Problem with Manipulate. Michael E2 suggested on the ...
2
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0answers
62 views

Strange Integrate messages / $RecursionLimit being ignored

Introduced in 10.1.0 The following behavior was observed in Mathematica 10.1 (Windows 64 bit) When attempting to evaluate the following integral, Mathematica outputs several messages which appear ...
2
votes
0answers
89 views

How can I do multiple (double) integral with periodic boundary conditions?

I am trying to do a simple double integral $\int_0^l \left[\int_0^l h^3 h_{xxx}dx\right]dx$ with periodic boundary conditions $h[0,\tau]=h[l,\tau]$ $h_x[0,\tau]=h_x[l,\tau]$ ...
2
votes
0answers
81 views

NDSolve is running an extremely long time: how can I save the existing data?

I am trying to solve a PDE by the following code. It takes 1 hour or so to reach t=25.72 but about 20 hours to reach t=25.72404031638060174049337306126853310997. Actually, the time step is extremely ...
2
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0answers
69 views

Integrate with Subscript: does this crash your kernel too?

I encountered some strange behaviour running v10.0.1 on a Mac Pro, while working with Integrate and Subscript. Starting from a ...
2
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0answers
97 views

Result of symbolic integration changed drastically by making assumptions

I would like to know the underlying reason for different outcomes for the two integration operation below. One of them includes a few assumptions, otherwise both have the same integrand: ...
2
votes
0answers
315 views

Symbolic matrix calculus: What's new in Version 9

I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ...
2
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0answers
119 views

Integration of UnitStep or HeavisideTheta

I am using Mathematica 9. If I evaluate Integrate[Piecewise[{{1 - r, r > 0 && r < R}}, 0], r] then I get ...
2
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0answers
189 views

How to prevent simplification of hypergeometric functions resulting from integrations?

Definite integrals from 0 to Infinity over a product of two hypergeometric (including exponential, trigonometric, hyperbolic, ...
2
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0answers
299 views

Derivatives of list elements

Could someone explain the odd behavior of the Derivative function when drawing arguments from lists? We have, ...
2
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0answers
184 views

About calculating Integrals

I am trying to Integrate the following Integral (all of the variables are reals) $$\int Exp(-(\cos^{-1}\left[\frac{\text{n}_0 (\text{v}_0-\text{x}_0)+\text{n}_1 (\text{v}_1-\text{x}_1)+\text{n}_2 (u ...
2
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0answers
382 views

Simple contour integral with a parameter gone wrong

I run into the following problem, I tried to evaluate a very simple integral: Assuming[ a > 0 , Integrate[Sin[a*s]/(s - I)^2, {s, -Infinity, Infinity}]] ...
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0answers
45 views

Minimax for conditioned UnitStep functions

I made a simplified version of my problem, and I have now: ...
1
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0answers
93 views

How can I improve the solution of my PDE?

I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
1
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0answers
43 views

Multiplying two sets of data (x,y values, but different x density) followed by integration of the product

I've been trying to do this by myself today, but no luck yet. Please, see attached image. Basically, I do have two data sets A (x1,y1) and ...
1
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0answers
135 views

Mathematica can't, or won't evaluate an integral (again)

I'm relatively new to Mathematica and really need some help here to spot what's going wrong with my integration issues; Mathematica doesn't evaluate my integral, after a fair amount of time running, ...
1
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0answers
70 views

Derivative with respect to a tensor

I am trying to differentiate a tensor with respect to another one in Mathematica, but I can't do it. Down below is the code I am using: ...
1
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0answers
57 views

MacDonald formula for Modified Bessel Functions

Mathematica seems to not know these two integrals: $$\int_0^{\infty} e^{-x \cosh{\xi}} d\xi = K_0(x)$$ $$\int_0^{\infty} e^{-\frac{1}{2} \Big( \frac{x y}{u} + u \frac{x^2+y^2}{x y} \Big) } K_{i t}(u) ...
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0answers
57 views

Order of integration resolves “Indeterminate expression encountered.”

Bug introduced in 10.0.0 and fixed in 10.0.1 Today I came across the following integral: ...
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0answers
107 views

Giving hints to Integrate

I working with the integral ...
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0answers
88 views

Help wanted in evaluating an integral

Trying to evaluate an integral. To be specific, I'm trying to find the expectation value of $x^2$ for the ground state of hydrogen. Here is the code I used: ...