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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2answers
89 views

A possible error related to the evaluation of a double integral

According to the Mathematica, the integral below NIntegrate[ Log[Log[1/(x y )]] Log[1/(x y )]^(-0.5 - 1), {x, 0, 1}, {y, 0,1}] might possibly evaluate to ...
4
votes
1answer
246 views

Asymptotic expansion

I wanted to expand a function of $x$ about $x=\infty$ and see its coefficients as a function of the parameters $m,n,q,y$ and I wrote this - but it didn't work! It gave me back a very complicated ...
0
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0answers
61 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
votes
1answer
45 views

Integral not being evaluated

I'm trying to do the following integral, but Mathematica won't evaluate it - it just spits out the actual symbollic integral (sorry I'm not sure how to copy the output into this post so it appears as ...
1
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0answers
119 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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1answer
57 views

Extension of harmonic number to the real domain

What is exactly the domain of validity of the identity: Sum[1/(k + j - 1), {j, 1, i}] == HarmonicNumber[k - 1 + i] - HarmonicNumber[k - 1] when ...
3
votes
1answer
174 views

Convergence in NIntegrate vs Integrate

I am faced with this situation that for a certain integration, $\int _0 ^\infty \frac { \tanh (\pi \sqrt{x} )} {\sqrt{x+10} } dx$ - the command Integrate returns ...
1
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1answer
167 views

Can ParametricNDsolve be used for coupled PDEs with 5 parameters?

I have a system of coupled PDEs with five parameters that I only know ranges for rather than explicit values, and I was wondering if I could define a parametric equation with ParametricNDSolve and ...
0
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2answers
148 views

How to numerically integrate this integral?

I want to integrate the function funcin (spherical coordinates). ...
18
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0answers
232 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: ...
1
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1answer
81 views

Poor performance when evaluating double integral of hat functions

I am trying to evaluate a double integral but am having performance issues. First a bit of math I am using a Galerkin like scheme to discretize operators in an equation I am working with. The ...
3
votes
1answer
86 views

How to calculate the residue of $1/f(z)$ at a numerical approximation to a root of $f(z)$?

The input Residue[1/DirichletL[19,10,s],{s,s0}] gives 0 even when s0 is a root. For ...
0
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3answers
285 views

Solving an Integral Numerically

I have been trying to solve the integral equation below, but cant seem to find a way out of this. Can someone please help me out with suggestion? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
1
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1answer
76 views

About an elementary limit

Here we have an elementary limit that Mathematica simply doesn't want to compute it. What solutions might I have to fix that? Could you help here? As you can easily guess, the limit is precisely $0$. ...
3
votes
2answers
180 views

How to find the maximum of this function on the positive real line?

I need to maximize this function on the positive real line: $$ \frac{1}{\Gamma(x)^{14}}\cdot\frac{1}{{\frac{323.6}{14x}}^{14x}}\cdot(1.22578*10^{19})^{x-1}e^{-14x} $$ the correct answer should be ...
0
votes
1answer
96 views

Mathematica does not solve this integral [closed]

I want to compute the integral of a polynomial in t, which I know an analitical solution exist. But Mathematica give me as result the input, not the result of the integral: I already know this ...
4
votes
2answers
113 views

Inconsistent results for equivalent converging symbolic integrals

I have looked at previous questions and I'm aware that this seems to be a known bug: Mathematica giving inconsistent results for symbolic integrals done in different ways. The origins for the bugs ...
6
votes
2answers
161 views

Fundamental Theorem of Calculus for definite integrals… assume continuity?

So here's the problem: I can evaluate the indefinite integral: Integrate[D[u[x], x], x] u[x] However, I'd like to ...
0
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1answer
52 views

Excluding an interval of parameters from Integrate [duplicate]

I'd like to compute an integral that depends on a parameter, but I'd like to exclude an interval from the computation. For concreteness, say I want to compute ...
3
votes
2answers
112 views

About the wrong evaluation of an integral

Here is an integral I've been studying in my research and I've just realized that Mathematica $8.0$ is unable to correctly compute it. I have 2 simple questions to ask: $1)$. Is my code below ...
5
votes
1answer
173 views

Simplification of integrals depending on a parameter [duplicate]

Assuming[Element[n, Integers], Integrate[Sin[x]*Sin[n*x],{x,0,Pi}]] returns 0, which is obviously wrong for n=1. ...
4
votes
1answer
567 views

Is it possible to calculate a Lebesgue integral in Mathematica?

As the title says, I wonder if it is possible to calculate a Lebesgue integral in Mathematica, especially when the domain of integration is $\mathbb{R}^N$, or in other words multivatiate Lebesgue ...
3
votes
1answer
85 views

Problem with limit that requires L'Hôpital's rule to compute

Consider the following limit. Limit[(a - Sqrt[a^2 + x])/(a^2 - a*Sqrt[a^2 - x]), x -> 0, Assumptions -> {a > 0}] Mathematica 9.0.1.0 gives ...
1
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1answer
162 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 ...
1
vote
1answer
153 views

Numerical saddle point problem of a function of many variables

I want to find the following saddle point of the function of 10 variables: . I am not able to find the stationary points by setting the first derivatives to 0, so I need do optimize the function ...
10
votes
2answers
263 views

How to take derivative of parameterized coordinate?

Suppose I have a vector in $\mathbb{R}^n$ but $n$ is not known in advance. I want to be able to write functions which operate on the components of that vector, and then I'd like to be able to take ...
1
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1answer
151 views

I want change gamma function form into beta function form

I want to integrate below form ...
0
votes
1answer
62 views

One more question about Assumptions and Integrate

There are many questions about assumptions here. Many of them are problem specific. That is why I want to ask a question in the most general way. Why does Mathematica solves this ...
4
votes
3answers
249 views

Creating a function with integral zeroes of the 0th, 1st, and 2nd derivatives

I would like to be able to randomly generate functions, each of which satisfies $f : [-10, 10] \rightarrow [-10, 10]$ All the zeroes, critical points, and inflection points have an integral ...
1
vote
1answer
201 views

Error Function Integral (Erf)

Any idea how to solve analytically this integral Integrate[(a Erf[a Sqrt[b/(a^2 + b)] c])/(a^2 + b)^(3/2), a] I tried substitution u=a^2 + b, but it didn't work. ...
-6
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1answer
126 views

Alternative closed forms for digamma expressions

What commands should I use such that Mathematica / W|A express $$\psi(1+i)+\psi(1-i)$$ exclusively in terms of trigonometric functions?
0
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0answers
70 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
votes
0answers
88 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: ...
1
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2answers
77 views

Unknown limit of an array of area integrals

Could someone explain why Mathematica can't finish computing this limit (this is a limit of an array, when n -> Infinity (n ...
1
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1answer
107 views

Improper mutiple integral

I would like to solve the following integral: ...
0
votes
0answers
79 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. ...
5
votes
2answers
337 views

Double integral over a parallelogram

Problem: Evaluate the following double integral $$\int \!\!\! \int_D (14 x^2+61 xy+42 y^2)^{3} \, dxdy$$ where $D$ is a parallelogram between these four lines: $2x+7y=6$, $2x+7 y=-6$, $7x+6 y=6$ and ...
3
votes
1answer
279 views

A Bessel & Struve functions related integral

I try to numerically compute this integral and I don't figure out why on earth Mathematica is not able to do it. Is my input correct? Does it possibly have a closed form? ...
0
votes
3answers
105 views

How to remove the 1. when differentiating 0.5x^2

My question is very basic, When using the Differentiate functionality of Mathematica in this way: D[0.5 x^2, x] This results in: ...
2
votes
2answers
174 views

Another fractional part related question

Having known the fact that the evaluation of the integrals containing fractional parts often contains errors, I wonder if the integral below possibly evaluates to $0.7$ or this is just a coincidence ...
1
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1answer
214 views

Calculating electrostatic potential from arbitrary charge density

In electrostatics, one often desires to know the electrostatic potential generated from the outside of a charge distribution; however, I am interested in finding the electrostatic potential inside of ...
0
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0answers
62 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 ...
1
vote
1answer
103 views

Help with finding solution for utility function [closed]

I'm brand new to Mathematica and having trouble finding a solution for Lh based on the first order condition. I'm not sure if it is something I'm doing in Mathematica or something wrong with the ...
0
votes
1answer
118 views

Revolving the area between two functions about an axis

I'm trying to graph the revolution of the area between two functions about an axis, but I'm new to Mathematica, and not sure how to proceed. My area is defined by ...
4
votes
2answers
298 views

Using units and piecewise functions in Integrate

For simple cases, Quantities appear to be handled well by Integrate: ...
0
votes
1answer
43 views

Showing result of derivative and other functions [closed]

I have a problem with my Mathematica 7.0 When I write: Derivative[x^2, x] Mathematica returns as result : ...
0
votes
2answers
141 views

NDSolve boundary query / Extracting values from solution

I have a function $O_{2}$ with boundary conditions $O_{2}(r_{o}) = p_{o} $ and $O_{2}(g) = O_{2}'(g) = 0$. I plot it using the solver code below; ...
0
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1answer
62 views

Different integral when used with assumptions

I want to calculate an integral, but Mathematica gives me different results if I am more specific with the Assumptions option of ...
5
votes
2answers
194 views

Triple fractional part-related integral

The evaluation with Maple suggests the triple integral is around $1$, but Mathematica tells it's $0.0958758$. When using the code ...
5
votes
1answer
159 views

Working with a system of differential equations that cannot be solved explicitly

I have to work a lot with three functions $\;o_1(t), o_2(t), o_3(t)\;$ that are solutions to the certain system of differential equations: ...