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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-1
votes
1answer
86 views

how can use $\mathop {\lim }\limits_{x \to 0} \frac{{e^x - e^{\sin \left( x \right)} }}{{x - \sin \left( x \right)}}$ [closed]

How can calcul $$\mathop {\lim }\limits_{x \to 0} \frac{{e^x - e^{\sin \left( x \right)} }}{{x - \sin \left( x \right)}}$$
1
vote
0answers
420 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, ...
0
votes
1answer
226 views

How to make Mathematica show intermediate steps in integral [duplicate]

I want to know how Mathematica evaluates this integral: $PV \int _ {0} ^ {i \infty} d \tau \, \frac{e^{-\frac{\tau^2}{2 M^2}}(b^2 - 3 τ^2)^2 (|b^2+\tau^2|-(b^2-\tau^2))}{\tau (\tau^2 - b^2)}$, where ...
0
votes
1answer
170 views

Solving Integro-Differential equations

I need help solving this equation. Is there a built in function that solves this type of equations? DSolve wouldn't work. Updated equation: ...
0
votes
2answers
213 views

Why does FindMinimum return 'The function value Null is not a real number'?

I am working with the following function ...
3
votes
1answer
244 views

Series approximation to integral

I would like to approximate the integral $$ \int_0^\infty dy\,\frac{1}{\sqrt{2\pi y\sigma^2}}\exp\left(-\frac{(x-y)^2}{2y\sigma^2}\right)f(y), $$ as a series expansion in the limit $\sigma\rightarrow ...
2
votes
1answer
120 views

Calculate exact Probability of product of normal random variables

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Normal Distribution having location parameter $\mu_{10\times 1} = ...
1
vote
2answers
209 views

Differentiation of an unknown function

I have to take the partial differentiation of an unknown function. For example, take the unknown function to be $g(x)$. Then it's derivative w.r.t $x$ is $g'(x)$. By default, Mathematica ...
2
votes
0answers
89 views

Getting error messages from a Plot expression containing an integral [closed]

This should be a really simple question, but I just got confused. Plot[Integrate[x, x], {x, -5, 5}] Integrate::ilim: Invalid integration variable or limit(s) ...
-2
votes
1answer
78 views

Help me with sum [closed]

good morning $$ \begin{array}{l} \left\{ \begin{array}{l} u_0 = 1 \\ u_n = 3 - \frac{4}{{1 - v_n }} \\ \end{array} \right.\quad \\ \;v_n = \left( { - 3} \right)^{n + 1} \\ s = v_{1436} ...
6
votes
2answers
486 views

Integral does not converge (when it should) [duplicate]

Bug introduced in 10.0 and fixed in 10.0.2 I was looking at integrals like: Integrate[HermiteH[50, x]*Exp[-x^2], {x, 0, Infinity}] which gave me a "does not ...
0
votes
1answer
101 views

Operator product

I have this problem: I define the gradient operator as: gradiente = {D[#, x] &, D[#, y] &, D[#, z] &} Now, if I want to apply the operator on a ...
0
votes
1answer
74 views
0
votes
1answer
122 views

Integrating spherical harmonics

I am trying to simply check the integration/normalization condition on the SperhicalHarmonic functions that are built into Mathematica. So basically, I just want to check that the following integral ...
2
votes
1answer
121 views

Double integral over normal pdf gives inconsistent answer

I am using Integrate function to do the following double integral ...
1
vote
1answer
74 views

Performance boost for definite integration with symbolic limits

In Mathematica, the symbolic definite integration ...
2
votes
0answers
82 views

Evaluating an integral

Here is the input: Integrate[E^(2 I*t)/(2*Pi*(E^(I*t) - z)), {t, 0, 2 Pi}] and here the output: ...
2
votes
0answers
106 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 $h[0,\tau]=h[l,\tau]$ $h_x[0,\tau]=h_x[l,\tau]$ ...
0
votes
2answers
99 views

Derivative after numerical Integration

So I have a function that I want to numerically integrate with respect to temperature, so the integral changes depending on the value of temperature being used as it is one of the bounds. After ...
2
votes
1answer
125 views

Limits and transformation rules

I can calculate this limit: Limit[(c^(1 - g) - 1)/(1 - g), g -> 1] and obtain the correct value: Log[c] but if I try ...
0
votes
2answers
133 views

What is the simplest way to plot x^(1/3) on the interval [-3,3]?

My question is: What is the simplest way to plot x^(1/3) on the interval [-3,3]?
4
votes
2answers
116 views

Adding assumptions changes the result of Integrate

When I try to calculate the following integral: ...
2
votes
1answer
112 views

How to avoid complex terms in the results given by Integrate?

As shown by In1, integrating Sqrt[x^2 - 1]/(a + x^2) (1/x) returns a result with a complex terms; however, after I make a ...
2
votes
0answers
152 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 ...
0
votes
1answer
146 views

Replacement of terms/Pattern matching involving products of derivatives of a function

In delving into Ramanujan summation, I'm trying to get a hold of the relations of the form $$\sum_{n=0}^\infty f(n)=\dfrac{h\frac{d}{dx}}{{\mathrm{e}^{h\frac{d}{dx}}}-1}\int_{0}^\infty ...
4
votes
4answers
447 views

$L = \lim\limits_{z \to 1} \frac{1-z}{1-z^\ast}$ evaluates incorrectly

I'm about 90% certain this is a Mathematica issue, not me making a silly mistake. I'm trying to evaluate $$L = \lim_{z \to 1} \frac{1-z}{1-z^\ast}.$$ Naively entering ...
6
votes
1answer
240 views

Incorrect evaluation of integral involving a DiracDelta, whose argument has infinitely many zeros

Let's say $X>0$ is a random variable with probability density $p_X(x)={\rm e}^{-x}$. Define the random variable $Y=\sin(X)$. From the transformation theorem for probabilities we know that its ...
1
vote
1answer
103 views

Strange timings of integrals involving Hermite's polynomials

I have used Mathematica to calculate tunneling for quantum harmonic oscillator. The code is simple: ...
1
vote
2answers
94 views

Integrating a compound expression

I have an integral of the form I[r]=∫(arExp[-r]-brSin[k(r-d)]Exp[-r])BesselJ[0,kr]dr where Besse1J[0,kr] is the modified ...
1
vote
1answer
141 views

Mathematica is able to compute an indefinite integral but not the corresponding definite one

I'm trying to compute the following definite integral (μ is a parameter): ...
8
votes
2answers
660 views

Probability: Calculating a multiple integral

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=2,5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Cauchy Distribution having location parameter $\mu_{10\times 1} = ...
5
votes
3answers
406 views

Bug in complicated Limit

The code Limit[Log[2 - Sin[x]*Cos[x]], x -> Infinity] outputs Interval[{0, Log[3]}] in Mathematica 10.0.2.0 . It should ...
3
votes
2answers
602 views

Color a Function by its Derivative

Mathematica's ColorFunction seems to struggle with coloring a function "y" by its derivative D[y,x]. This is a seemingly simple task, but Mathematica can't handle it. While I can certainly evaluate ...
4
votes
1answer
101 views

Products of Differential Operators

I have a differential equation defined as the product of operators which I want to expand out into a polynomial in powers of $z\frac{d}{dz}$ $\qquad \prod_{n=1}^p(z\frac{d}{dz}+a_n)$ However when I ...
0
votes
1answer
70 views

Integration of an expression yields wrong result

I'm trying to find a general expression for the definite integral of ...
2
votes
2answers
271 views

After definite integration the result is still integration variable dependent!

This integral $\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\frac{\exp \left(\frac{2}{x^2+y^2+z^2+1}-2\right)}{\left(x^2+y^2+z^2+1\right)^4}dzdydx$ or ...
-3
votes
1answer
71 views

NDSolve a differential equation depending on some parameter

I have to solve the differential equation, to get a plot of T and R, ...
3
votes
1answer
967 views

Calculating the area under a curve

How can I calculate the area under a curve after plotting discrete data as per below? ...
1
vote
3answers
206 views

Speed up NIntegrate, which takes eigenvalues from another function

I have simplified my problem here, in my actual problem the matrix is much bigger which makes it impossible to find eigenvalues analytically. So, I chose standard BCS problem (2x2 matrix) to ...
0
votes
1answer
63 views

Derivatives of overscript variables

If we have an expression with terms of some variable and terms of the same variable with some overscript, the differentiation of this expression does not entirely function. The problem is that ...
-1
votes
1answer
153 views
4
votes
2answers
282 views

Integration of a Rational Function returns RootSum[]

I am trying to solve an integral given below: Integrate[r^2/(-α r^3 + r^2 - 2 m r + Q^2), r] but since coefficients of this cubic polynomial are as parameters, ...
8
votes
4answers
394 views

Definite integral incorrectly giving a nonreal value

fixed in 10.1 (windows and Mac OS X) In Mathematica 10.0, when I enter N[Integrate[Sqrt[1+x^3],{x,-1,3}]] I get a nonreal value (i.e., the imaginary part is ...
0
votes
2answers
84 views

A simple integral operation

Evaluating the following expression results in a non-zero output FullSimplify[Integrate[2 f[x], {x,0,1}] - 2 Integrate[f[x], {x,0,1}]] I think the output should ...
1
vote
1answer
147 views

Partial differentiation mixes up variables

Consider $$ U \equiv \dot{\theta} - \theta \ ,$$ where as per usual $\dot{\theta} = \frac {d \theta}{dt}$. We then have $$ \frac {\partial U}{\partial \theta} = -1 \quad , \quad \frac {\partial ...
2
votes
1answer
180 views

Complex Integration

There are some sequential functions: ...
9
votes
1answer
231 views

Suspected bug in Integrate

Bug introduced in 9.0.1 or earlier and fixed in 10.1.0 In version 10.0: ...
0
votes
1answer
174 views

Get rid of Error Function: How to get rid of sequential appearances of error function?

We have a function as e[t_] :=(E^(-t^2)) Cos[0.1 t] and we must evaluate below integration (However I used the variable x ...
2
votes
1answer
109 views

How to check if Integrate solved the integral?

This seems something that must have been asked before, but I am not able to find something. Integrate does not return status nor throw error when it can't find antiderivative. It just returns the ...