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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-3
votes
1answer
69 views

How to symbolically integrate 2D exponential function? [duplicate]

Is it possible to symbolically solve a 2D integral of the following form $$\int d \vec{r}e^{-\frac{\left| \vec{r} - \vec{r}' \right|^2}{2c}}e^{-i \vec{k} \cdot \vec{r}} $$ where $\vec{r} = (x,y)$ and ...
1
vote
1answer
43 views

NIntegrate::inumri: error [on hold]

I am getting the following error: NIntegrate::inumri: The integrand c (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- (1+Times[<<2>>])^0.5)) (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- ...
2
votes
2answers
143 views

Symbolic vs numerical integration

This is related to a question that I asked before but didn't resolve quite well. I want to obtain the solution of the following expression analytically: ...
0
votes
0answers
53 views

Product of two Meijer's Function

I want to evaluate an integral $I_1$ defined in $Eq.(1)$ as \begin{align} I_1=\int_{0}^{\infty}\frac{x\exp(-\beta x)K_1(\alpha x)}{1+x}dx\tag{1} \end{align} Where $\alpha\geq0$, $\beta\geq0$, and ...
1
vote
0answers
29 views

Hidden assumption in Mathematica integration [duplicate]

If I do Integrate[Exp[I*omega*t],t], it gives me $\frac{1}{\omega} e^{i \omega t}$, as expected in most of the cases, except when $\omega$ is 0. Mathematica seems ...
0
votes
1answer
38 views

Plotting a function based on complicated integral

I have this function : f[Lambda_] := K Integrate[x Exp[- x^2-Lambda x] HypergeometricU[-Lambda,1/2,(x+ Lambda/2+2)^2],{x,0,Infinity}]; where ...
3
votes
1answer
68 views

Euler-Maclaurin summation

I want to compute asymptotic approximations to partial sum of harmonic series in Mathematica, using Euler-Maclaurin summation formula. ...
0
votes
0answers
62 views

How to evaluate this integral with a bessel function

I have to evaluate this integral, Sin[θ] 2 π BesselJ[0, k Sin[θ] (μ[j] - μ[i])] Exp[2 k^2 σ^2 Cos[θ]^2], wrt $\theta$ between the interval [0, $\pi$]. The ...
0
votes
1answer
56 views

How to calculate the derivative at a point of a non-integrable multivariable function?

I want to integrate this function with respect to θ1 and then take the derivative of that function with respect to n. Since the ...
2
votes
1answer
42 views

Why do Wolfram Alpha and Mathematica give different answers? [closed]

I've just got my hands on Wolfram Mathematica and tried to see if I can figure out how to use it by myself. I've plugged in an integral $\int \frac{dx}{(1-x^2)^{2/3}}$, knowing that the result is ...
2
votes
1answer
106 views

Problem with Volume [closed]

A bug probably. This should give the volume of the unit sphere: vol = Volume[{1. r, th, ph}, {r, 0, 1}, {th, 0, Pi}, {ph, -Pi, Pi}, "Spherical"] but it gives: ...
4
votes
1answer
86 views

Finding Euler spiral convergence point for powers other than 2

I'm playing around with Euler spirals, using a variable power to see how the plot changes, $ \left\{\begin{matrix} x = \int_0^s \cos \left ( s^n \right ) ds \\ y = \int_0^s \sin \left ( s^n \right ) ...
1
vote
1answer
59 views

Wrong Limit[…] for inexact expressions

I noticed that Limit can return nonsense when using inexact parameters. In the following code, a is my (exact/inexact) ...
2
votes
2answers
122 views

A simple question: Input problem

I have a simple problem. First I define the value of variables, then I calculate the expression as the following: Code 1: ...
1
vote
2answers
110 views

How to get the $0$ result for this limit?

Consider the following series: $$\sigma (\text{x$\_$})\text{:=}\sqrt{\sum _{k=0}^{x-1} \frac{(x! x!) (-1)^{x-k}}{(x-k) (k! (2 x-k)!)}+\frac{\pi ^2}{12}}$$ From the following codes, it seems that the ...
0
votes
0answers
28 views

How do I numerically integrate the result of NDSolve if it depends on several variables?

I am trying to numerically integrate solution of NDSolve. I am trying to integrate my result of NDsolve in line 97 of my notebook, but am getting the error ...
1
vote
1answer
51 views

The assumption in integration does not work?

I am new to mathematica. Here is the question. I try to do the following integration with the assumption that k1<0, k2<0 and k1,k2 are real number. However, the result includes \sqrt{k1}? ...
4
votes
1answer
86 views

Pertubation series of given equations

I would like to define a function that does the following. If I have an equation, for example: $$f(x)+[1-f^2(x)]+f^{\prime\prime}(x)+f(x)\ f^\prime(x)=0$$ and I am given a value for $f$ to expand ...
0
votes
0answers
15 views

Integration with IntervalMemberQ

I define an interval and its associated index function. ...
0
votes
1answer
54 views

Integrate over FindRoot solutions

I have a function of bivariate normal PDF and its marginals defined as ...
0
votes
2answers
70 views

Expression which should be real-valued appears to be complex-valued [closed]

I want to plot the answer of the following integral: Λ = 10; Ω = 10; t = 1; Integrate[ω E^(-ω/Λ) Sin[(ω + Ω)t/2]^2/(ω + Ω)^2, {ω , 0, ∞}] The answer of ...
4
votes
6answers
871 views

Randomly Multiply OR Divide by a Random Number?

I want that Mathematica decides randomly if a given variable, gets multiplied or divided by a random number in a given range. The "naive" idea to just use ...
2
votes
2answers
131 views

Confirmation of a nice closed form

Can Mathematica 10 confirm a nice closed form for ...
-1
votes
2answers
64 views

Gradient of interpolated 3D data in mathematica 9

tt = Flatten[Table[{x, y, z, btot[x, y, z]}, {x, -1, 1, 0.1}, {y, -1, 1,0.1}, {z, -1, 1, 0.1}], 2]; ff = Interpolation[tt] Till here it is working fine as it is ...
0
votes
2answers
126 views

How can I solve this integral analytically?

I want to solve the following integral: Integrate[( E^(-ω/Λ) Sin[((ω + Ω) t)/2] Sin[(ω t)/ 2])/((ω + Ω)/4) , {ω, 0, ∞}] But unfortunately Mathematica cannot ...
2
votes
0answers
86 views

Why Can't Mathematica Integrate this? [closed]

I am trying to integrate Absolute-value functions from Wikipedia: ...
5
votes
2answers
188 views

Results in terms of a function

Let's assume I have a function $f(x)=\exp(10x^2)$, i.e. f[x_]:= Exp[10*x^2]. When I differentiate $f$ by evaluating the expression ...
1
vote
1answer
47 views

Differential Equations and Unit Notation

What do I get the Syntax::sntxi: Incomplete expression; more input is needed . error when I try to use the math palette for derivatives? What does the dot in 10. Farad Micro Volt mean? ...
1
vote
1answer
93 views

Use Meijer-G function to represent elementary functions

I want to represent these elementary functions: $x^{2}\sqrt{x}$, $\sin{4x}$, and $x\ln{x}$ as cases of MeijerG. What arguments should I give to ...
-1
votes
1answer
54 views

Taylor and Maclaurin series [closed]

I need to calculate limit of sin(x)*cot(tanx) at 0 using Maclaurin series I took the usual approach but did not get anything of help.
3
votes
3answers
119 views

Limit n->Infinity of recursive sequence

I have defined a recursive sequence a[0] := 1 a[n_] := Sqrt[3] + 1/2 a[n - 1] because I want to calculate the Limit for this ...
5
votes
5answers
119 views

How to find the derivative value at $(\pi,0)$ for this implcit function $n$ times?

I am trying to take the implicit derivative at $\sin(x+y)+\sin(x)=y$ and substitute $x=\pi$ and $y=0$ at least 6-7 times since I need to find the Taylor series for this function. Since I barely ...
0
votes
0answers
62 views

How to evaluate this integral

I am trying to evaluate the following integral in Mathematica: ...
0
votes
1answer
43 views

Same integral gives different results with assumption

b = 1 k = 12560 r = 500 res = Integrate[Exp[I*k*x*Sin[o]]/(r + x*Sin[o]), {x, -b/2, b/2}] resab = Abs[res]^2 Plot[resab, {o, -Pi/20, Pi/20}, PlotRange -> Full] ...
0
votes
0answers
15 views

How to solve this system of Partial Differential Equations [5] [migrated]

$${\partial z \over \partial x}f(x,y,z)+{\partial z \over \partial y}g(x,y,z)=h(x,y,z) $$ $${\partial z \over \partial x}F(x,y,z)+{\partial z \over \partial y}G(x,y,z)=H(x,y,z) $$ ...
0
votes
0answers
33 views

Integration of a Gaussian function in kernel density estimation

I came recently across an odd result of mathematica, which so far I cannot explain. In a standard kernel density estimation (example http://www.ssc.wisc.edu/~bhansen/718/NonParametrics1.pdf) the ...
1
vote
1answer
113 views

DensityPlot showing artifacts [closed]

This is my first post on Mathematica.SE, and I'm still a bit new to Mathematica. I believe I'm probably doing something silly in my code, but I have not been able to find where. I'm trying to plot a ...
3
votes
0answers
80 views

Inconsistent results for symbolic trigonometric integral

I am trying to evaluate (on Mathematica v.9) the integral \begin{equation} \int_0^x [\sin (x) \sin (2 y)-\sin (2 x) \sin (y)]^t \,\mathrm{d}y, \end{equation} where $t$ is an even, positive integer. ...
0
votes
0answers
68 views

What is the function in Mathematica that can be used to find the derivative of a constant value function with respect to an arbitrary matrix?

I have a function that consists of some matrices. This function results in a constant value. I need to take the partial derivative of this function with respect to one of the matrices it depends on. ...
3
votes
0answers
84 views

Bug or feature? If statement inside double integrals

(taken from http://math.stackexchange.com/questions/1592901/bug-or-feature-if-statement-inside-double-integrals) Generally speaking, $$ \int_c^a f(x) dx = \int_c^{a-b} f(x) dx + \int_{a-b}^a f(x) ...
4
votes
1answer
79 views

Somewhat Irreproducible Integrate Results

Backslide introduced in v10 and persisting through v10.3.1. In the course of considering question 102922, I encountered erratic results from a particular integration. It is illustrated as follows. ...
2
votes
1answer
96 views

Limit $\sqrt{3-x}$ as $x\to3^+$ [closed]

I'm trying: $$\lim_{x\to3^+}\sqrt{3-x}$$ Using real numbers, technically this limit does not exist. However, Limit[f[x], x -> 3, Direction -> -1] I also ...
5
votes
2answers
147 views

Symbolic integration of SphericalBesselJ

Backslide introduced in v10 and persisting through v10.3.1. Consider the following integral ...
0
votes
0answers
64 views

Finding double inverse Laplace transform numerically

Edit: I asked Prof. Valko, he was so nice to point out where the mistake is. The problem is solved ! Thank you for your attention ! Recall the the double Laplace transform of a function $f(x,t)$ is ...
0
votes
1answer
85 views

Integrating the derivative of a function does not give expected result [closed]

I was trying to do the following integral: f[z_]:=Hypergeometric2F1[1,-a,1-a,1/(1-z)]/((1-z)^a-1) Integrate[D[f[z],z],z] I thought the result should be ...
5
votes
2answers
186 views

Can your Mathematica do the following integral?

Backslide introduced in v10 and persisting through v10.3.1. I was trying to do the following integral in Mathematica: ...
4
votes
0answers
102 views

Exploring formal limit definition

I found a few demonstrations on the Wolfram Demonstration Project site that help users to explore the formal definition of a limit. That is, $$\lim_{x\to a}f(x)=L$$ if and only if for every ...
8
votes
1answer
246 views

Strange bug: Product[1/(1-1/2^(n-1)),{n,2,Infinity}] = 0?

This infinite product is correct: Product[1/(1 - 1/2^n), {n, 1, Infinity}] (* 1/QPochhammer[1/2, 1/2] *) Numerical value of this result is not equal to zero ...
-1
votes
2answers
55 views

computing a limit [closed]

I couldn't compute this limit: it should be -3. I couldn't find the analytic way to compute it.
4
votes
1answer
91 views

Parametric numerical integration [closed]

I would like to solve the integral: $$ \iiint\frac{e^{-\sqrt{x^2 + k^2}}x^2 \sin{\theta}}{\sqrt{x^2 + k^2}} dx d\theta d\phi$$ defined in $x \in [0,+\infty]$, $\theta \in [0,\pi]$, $\phi \in [0,2 ...