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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1answer
72 views

Integrate does not accept my integrand expression

I want to calculate the symbolic integral, but I could not obtain the final results from Mathematica. ...
1
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1answer
135 views

Is it possible to give the closed-form of the stiffness matrix of triangular prism element?

Suppose the vertices of triangular prism are 1, 2, 3 (bottom triangle), 4, 5, 6 (top triangle), the coordinates of the vertices are $$ (x_i, y_i, z_i), i=1,2,3,4,5,6. $$ We can write the stiffness ...
0
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1answer
41 views

How to evaluate an integral involving normal distribution

I want to compute the following integral, in which 5 can be replaced by any natural number. But I found Mathematica keep running forever and cannot evaluate it. I want to ask for some help. ...
15
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0answers
143 views

Are greek symbols causing different evaluation?

I've updated today to Mathematica 9.0.1.0 from version 8 and found something that absolutely confuses me. Let us define a piecewise function: ...
11
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0answers
157 views

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

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

Why does Mathematica give an incorrect answer to this multiple integral?

This is not a new problem but I would like to understand why Mathematica gives the result that it does. (Volume of a hypersphere) ...
8
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0answers
183 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
468 views

Dual complex integral over implicit path using contour plot

Context I am interested in doing double contour integral over paths which are defined implicitely. For the sake of debugging, let's assume its $$\oint_{\cal C}\oint_{\cal C} \frac{1}{u\, x} d u d x$$ ...
6
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0answers
134 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
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0answers
158 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
112 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
169 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
131 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: ...
2
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0answers
141 views

Using WhenEvent for derivative of discontinuous function

I have a discontinuous function ($u(t)$, a square wave) and I would like WhenEvent to trigger when the signal goes high/low, i.e. when the value of $u(t)$ changes. ...
2
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0answers
115 views

Real integral evaluating as indeterminate

Mathematica evaluates the following integral as: ...
2
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0answers
118 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: ...
2
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0answers
169 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
142 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
120 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. ...
2
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0answers
209 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
236 views

How to plot function & integral with vector variable?

I want to plot functions & integrals with vector variable the present in this paper. For example the equation (5) at p. 3: I want to plot a chart like figure 5, i.e. the $x$-axis is the angle ...
2
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0answers
341 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
78 views

Limit of sequence

I tried to calculate the following limit $$\lim_{n\to\infty}n\sin(2\pi en!)$$ Mathematica gets ...
1
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0answers
78 views

how to do variation

I have an equation needs to do variation. I can do it by hand, but I get different result by mathematica. maybe I made some mistakes in programming. can anyone point out for me? thanks This is how I ...
1
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0answers
83 views

Simple Jacobians, Gradients, etc. with arbitrary length vectors/matrices?

Is there any way (or a package built for it) can do simple operations with vectors and matricies of arbitrary size, but conforming extents? For the simplest example to test, given an arbitrary vector ...
1
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0answers
57 views

Help with Integrals (and conditional expectations) of the Beta distribution: Integrate[e^(az) z^a (1-z)^b, {z, 0, 1}]

I have a Beta distribution, and am interested in calculating expectations and conditional expectations. The domain on the distribution is $z \in [0,1]$ Ignoring constants of proportionality, the ...
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0answers
100 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, ...
1
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0answers
142 views

Positive integrand giving negative answer

I'm integrating a positive function f(t) times sin(t) from 0 to pi/5 and get -38. Actually f is slightly negative for a short time (smallest value ~ -0.0005), but far from enough to explain this. ...
1
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0answers
221 views

Cauchy principal value integral of a list of numbers. How?

I have a list of numbers that are numerical samples of a function for which I need to find the Cauchy principal value integral. I thought I should be able to combine Interpolation with Integrate to do ...
1
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0answers
442 views

Calculating the mean curvature of a surface - suggestions

I am attempting to calculate the mean curvature [1, 2] of a surface defined by a function of x and y. My function is rather ...
1
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0answers
156 views

How to move differentation before the integral?

I have quite a lot expressions that need to be integrated after switching the integral sign with differentation operator. The additional problem is that the bounds are dependent to one of the ...
0
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0answers
44 views

problem solving a simple integral equation

I'm looking for a function q(x) so that integral( q(t) , t , x, x+2*pi/3) == a*sin(x)+b Could anyone help me on this one? Thx in advance
0
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0answers
42 views

Computing residues of matrix valued functions symbolically

I have a somewhat specific application in mind, but I've run into this kind of problem a few times and never found an elegant solution. Is there an efficient way to get Mathematica to recognize that ...
0
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0answers
46 views

Derivative of generating function (Example from documentation)

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

Numerical Differentiation of an interpolated list.

I have a synthetic spectrum with a wavelength range of .3 to .7 microns. I have interpolated this spectrum for re-sampling purposes. However, I am also attempting to calculate the first and second ...
0
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0answers
37 views

Errors while computing some terms of the Euler–Maclaurin formula

Here is an issue I came across while I was applying one of the well-known versions of Euler–Maclaurin formula. I try to realize why Mathematica goes wrong with this code below ...
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0answers
51 views

An error message with NIntegrate and inability to plot the integrand

I took a function of x which depended on parameters on m,n,a,y and then first summed up the n from -Infinity to Infinity and then I set the other parameters to some random values and then I asked it ...
0
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0answers
53 views

Exponential function Integral

I have tried to solve this integral: Integrate[E^(-((a^2 b c^2)/(a^2 + b)))/(a^2 + b)^2,a] Mathemathica is not able to solve it, I have tried the integration by ...
0
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0answers
63 views

Convergence problems with numerical integration of specific functions

I want to numerically integrate two functions that have several poles inside the integration region. These are the functions: ...
0
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0answers
72 views

Cannot calculate an integral

I am new to Mathematica. So I just run a basic procedure but Mathematica didn't calculate this integral. Maybe it is too complicated to be done. ...
0
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0answers
43 views

PDE syntax question

I am trying to solve a PDE of a reaction diffusion equation, and while I'm getting a decent looking solution, I am also getting inconsistent BC / initial conditions warnings and wanted to check if my ...
0
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0answers
62 views

Algebraic condition from a non linear equation

I have got a system of equations which look like this: $\theta_{1}^{2}e^{\phi_{1}\cos(\Omega z)}\tilde{w}\cos^{2}(\theta_{1}\sin\Omega z)\sin^{2}\Omega z+\frac{1-\lambda\cos(2\theta_{1}\sin\Omega ...
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0answers
48 views

Reducing a long complex expression to a simplier one by using assumptions

so I have an ugly looking equation that I wish to solve under some specific circumstances. Using DSolve I write; ...
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0answers
138 views
0
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0answers
92 views

Approximating a stochastic integral with a Wiener process

I would like some assistance to solve the following: $\sum\limits_{i=0}^{n-1} e^{-k(n\Delta t -i\Delta t)}\Delta z_i$ where $z$ is a Wiener process, $\Delta z_i = z((i+1)\Delta t)-z(i\Delta t)$. ...
0
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0answers
90 views

Non-Solvable PDE?

I would like to know whether this PDE is solvable and if yes, for which values of $a$. ...
0
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0answers
87 views

recurrence relations

If I write f[i_] := Expand[FunctionExpand[x^(i/5) LerchPhi[x, 1, i/5]]] for any i < 5, the result is a linear combination ...
0
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0answers
108 views

Strange result from integrate

I am working on the following problem. However, the first task takes too long, although the answer 0 is correct. In the second task, to reduce the calculation time, ...