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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
48 views

Plot $ g(r) = \int_0^\pi J_0(w\ r)\ \mathrm dw $

I want to plot $g(r)$ as a function of $r$ but $g(r)$ at each value of $r$ is an integral of the Bessel function over the the limits of $w$.
2
votes
2answers
66 views

Plotting a function $\psi(\rho,\theta,\phi)$ in spherical coordinates

If I want to plot the function $\qquad \psi(\rho,\theta,\phi)=\frac{1}{8}\left(\frac{1}{\pi}\right)^{1/2}\rho e^{-\rho/2}sin(\theta)e^{-i\phi}$, for which I wrote the code ...
0
votes
2answers
49 views

Global minimum of a function in a specified interval

I've got the following definition of fun1. epsilon = 10^(-8) fun1[h_] := (2 epsilon*Abs[Cos[1]]/h ) + (h*Abs[Cos[1]]/2) Let'...
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votes
0answers
25 views

Do these expansions make sense?

I mean Series[DiracDelta[x], {x, 0, 3}] $$ \delta (0)+O\left(x^4\right)+\frac{1}{6} \delta ^{(3)}(0) x^3+\frac{1}{2} x^2 \delta ''(0)+x \delta '(0)$$ and <...
0
votes
1answer
28 views

Model fitting for concave curve: test if asymptote or convergence exist

I am asking a double check if conceptually I set up proper model and proceeding in good direction to drive conclusions. I have a distribution that looks like this: I want to test if for increasing x ...
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0answers
50 views

Constructing a user function with an integral

Maybe this is a basic task to perform but I haven't found any literature. I am performing a convolution of two functions: ...
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2answers
50 views

Solving for upper bound of integral with known value

I'm trying to calculate the upper bound of an integral. My current code is f[r_?NumericQ] = (1/(Pi*a^3))*4*Pi*(r^2)*E^(-r/a); Plot[f[r], {r, 0, 1}] When I ...
1
vote
1answer
66 views

Tangent point in Polar Coordinates

I don't know which command to determine the tangent lines that are parallel to the line $x=0$ (i.e. the y-axis) in Polar Coordinates. Can you help me please to give me some suggestions? I attach some ...
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0answers
40 views

Indefinite integration of products of Bessel functions [on hold]

Is there any way to solve any of the following indefinite integrals in Mathematica? ...
0
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0answers
18 views

To prove F is irrotational and to find its scalar potential [closed]

F=(y^2 cosx+z^3)i+(2y sinx-4)j+(3xz^2)k Show that F is irrotational and find its scalar potential
1
vote
1answer
47 views

Strange behaviour in derivative of Floor function

The function Floor[x] is piecewise constant, hence its derivatives should be piecewise zero. This is far from true in Mathematica In[497]:= $Version Out[497]= "10.1.0 for Microsoft Windows (64-...
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2answers
37 views

Problem in dealing with Sign function

Let my function be $f(x)=e^{|x|}$. I wish to find $f''(x)$, this can be done as- $f'(x)=$sgn$(x)e^{|x|}$ $f''(x)=$sgn$(x)^2e^{|x|} =e^{|x|}$ In Mathematica, I am trying to plot $f''(x)$, it ...
2
votes
1answer
239 views

How do I label critical points on the plot of a curve?

I want to label the local maxima, local minima, and points of inflection on a plot of a curve. How is this done in Mathematica?
1
vote
2answers
59 views

Working with complex valued functions

I have a function which has real and imaginary parts and I need to differentiate both parts separately. This is a simpler example of what I have tried, without success: ...
3
votes
1answer
48 views

General integral does not match special case?

Consider the following function: f = (E^(2 I c \[Phi]) - (E^(2 I \[Phi]))^c) (E^(2 I \[Phi]))^n Integrating this function with respect to ...
0
votes
1answer
39 views

Relations between Function Variables in Computations

I have the relation λ=c/f, respectively f=c/λ and a simple function n[λ_]:=λ²+1. I'd like to differentiate the function with respect to f, then plot it as a function of λ again. For this, I can define ...
3
votes
1answer
152 views

How can I get the exact answer of the maximum of this function?

I am trying to find the maximum of a fuction: $ f(x)=\sqrt{x^2+9}-\sqrt{x^2-\sqrt{3} x+1} $. I tried Maximize[Sqrt[x^2 + 9] - Sqrt[x^2 - Sqrt[3]*x + 1], x] and ...
1
vote
0answers
38 views

Simplyfing a quotient of polynomials [on hold]

I am trying to simplify some quotient of polynomials. In this case, they are really easy but I will have to deal with way harder expression and I wanna know how to do it in full generality. An example ...
0
votes
1answer
59 views

Using “if” to compare 2 expressions (Complex and real numbers)

Hello. I want to solve this cubic equation and compare the answers then I can assing the lower result to "VmL" and the greatest result to "VmG" but I have problems when the result is a complex number ...
7
votes
1answer
173 views

Inconsistency in Mathematica of whether integral diverges or not?

Consider the following (beta function) integral Integrate[(1 - x)^a x^b, {x, 0, 1}] ConditionalExpression[(Gamma[1 + a] Gamma[1 + b])/Gamma[2 + a + b], Re[b]>-...
5
votes
1answer
72 views

Annulus distribution in n dimensions: normalising constant, normed mean and variance

I would like to know the normalising constant of a distribution which has the pdf, $$f(x) \propto \sqrt{\frac{1}{2\pi\sigma^2}}\text{exp}(-\frac{(|x|-r_0)^2}{\sigma^2}),$$ where $x\in\mathbb{R}^d$ ...
0
votes
0answers
25 views

NIntegrate failed to perform the integration unless AdaptiveMonteCarlo method is chosen

I have multi-dimensional numerical integration of some function depending on one parameter. If no specification for the integration method is chosen, the output for specific values of the parameters ...
1
vote
1answer
113 views

DiracDelta convergence in 3D - Cartesian vs. spherical coordinates

Integrating DiracDelta in 3D in Cartesian coordinates works just fine i.e. gives vecf[{x, y, z}] ...
1
vote
1answer
59 views

Plot of integral of summed `Sinc` series is incorrect

I have curve given by summing a small, finite series of Sinc functions, and I want to plot both the curve and its integral. In principle, it's easy: ...
0
votes
0answers
32 views

Gaussian probability distribution for a delta correlated variable [migrated]

I read in a paper that I have a vector $\bf{x}$ such that $$ \langle x_i (t) x_j (t')\rangle=\delta_{ij}\delta(t-t') $$ and the probability distribution for $\bf{x(t)}$ is a ...
0
votes
2answers
73 views

Continuous summation of a function [closed]

I have a simple function: func =x Sin[π x]^2 This creates a curve that oscillates between 0 and values that increase linearly ...
0
votes
0answers
12 views

Gaussian distribution for delta correlated random variables [migrated]

I read in a paper that "I have a vector $\bf{x}$ such that $\langle x_i (t) x_j > (t')\rangle=\delta_{ij}\delta(t-t')$ and the probability distribution for $\bf{x(t)}$ is a Gaussian ...
2
votes
1answer
34 views
1
vote
1answer
44 views

Eliminating Gamma from result of integration

I think the following integration result can be shown without Gamma. Can anyone explain Why Mathematica Uses Gamma. How to ...
2
votes
2answers
78 views

Integration with Bessel function as result

When I try to calculate this integral, 1/(2*Pi)*Integrate[ Exp[I*2*θ]*Cos[1/2 (7 + Cos[θ])], {θ, 0, 2*Pi}] Mathematica is unable to compute it. But the result ...
4
votes
1answer
87 views

Limit ArcTanh: different results in v10.4 and v11.3

I find a different results when computing limits with ArcTanh in version 10 and 11 of Mathematica. The problem emerges with the following function ...
0
votes
0answers
44 views

FullSimplify of Dirac Delta Function failed

I have t1 and t2 whose difference should be 0. But ...
0
votes
1answer
88 views

How can I assign first evaluate an Integrate command and then assign the integrated expression to a function?

I am trying to evaluate this integral? $$\int_0^1\int_0^1 \frac{\mathrm dt\mathrm ds}{(c^2 + 2se + as^2 - 2tf - 2tsd + bt^2)^2}$$ I tried to do using the definite integral, but these two didn't ...
0
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0answers
35 views

Residues of products

i have the following problem: My function is given by: $(cz^{-1}+aq^{-j}-bq^{-2j}z)\prod_{m=1}^{Q-1}\frac{qz-z_{m}}{z-z_m}+(-cz^{-1}+dq^{j}+bq^{2j}z)\prod_{m=1}^{Q-1}\frac{q^{-1}z-z_{m}}{z-z_m}=E$, ...
2
votes
1answer
86 views

How do I evaluate the limit of $(x-5+\sqrt{x+1})/\sqrt{x^2-9}$ as $x \to 3$? [closed]

I tried substitution first. It won't work for this one. When finding a limit of a fraction and in doubt, rationalize either the numerator or denominator.
0
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0answers
33 views

Correcting integration error by supplying assumptions

I wrote some auxiliary functions to help evaluate my main function ELC, which always return the error Unable to prove that integration limits {0, t} are real. ...
15
votes
6answers
780 views

Is there a workaround for this integral?

The command Integrate[Exp[a*Exp[I*x]], {x, -Pi, Pi}] produces ConditionalExpression[0, a == 0] which is not correct in view of ...
3
votes
2answers
112 views

Wrong Output for Limit

I want to calculate the following limit: ...
2
votes
1answer
100 views

How to compute many sums or tables efficiently

I have some questions about programming in Mathematica and I would really appreciate it if you could help me. I wish to plot the following function against the variable X, but to do this, first I ...
1
vote
1answer
81 views

Mathematica can't integrate my function [closed]

I was trying to calculate the definite integral $$ \int_0^.0076\int_0^.0425\int_0^.1275\frac{1}{x^2+y^2+z^2}\,dz\,dy\,dx $$ I entered this: ...
3
votes
2answers
32 views

How to use an imported table data in a calculation of f[x,y,z], where each row of the column correspond to x,y,z? [duplicate]

I have a table with desired inputs of a given function efvc[n,m,u]. I want to calculate for different values of n, ...
0
votes
3answers
91 views

Integration involving Bessel function and algebraic function

While trying to compute the following integrals, Mathematica is not able to do that. Any suggestion will be helpful. ...
0
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0answers
38 views

Analytic derivatives of LegendreP[a, z] w.r.t. a at a = 0?

I am interested in finding analytic expressions for various derivatives of the LegendreP[a,z] w.r.t. a at ...
4
votes
1answer
78 views

Tips for Complicated Indefinite Integrals

I would like to have an analytical expression for some complicated indefinite integrals (example below). I am able to solve these integrals numerically, and I am able to plot them in Mathematica, ...
0
votes
1answer
40 views

Replacing one of the integrals in the multiple integral with an analytical solution

Problem consist in simplifying complicated multiple numerical integral, where I know analytical solution for a subset of them. Integrand is of the form ...
3
votes
1answer
205 views

How can I solve the limit by mathematica?

I use the Limit and DiscreteLimit to solve it but failed. How to solve it by Mathematica? $$\underset{n\to \infty }{\text{lim}}n ...
1
vote
1answer
51 views

How to apply NIntegrate three times

I have following integration. $$I=\int_{0}^{\frac{\pi}{2}} \int_{0}^{\infty} \gamma e^{- \lambda \left(\gamma^2+2d\gamma\cos\theta -d^2 + \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} 2d\cos\Theta(d\cos\...
5
votes
1answer
82 views

Confusion in finding the definite integral

So, I'm new to Mathematica. I tried evaluating the following definite integral. However the answer i get from wolfram alpha & mathematica are different. Can someone please point out what I'm ...
2
votes
1answer
52 views

Taking a derivative of an eigenvector

I'm trying to calculate the derivative of an eigenvector that I obtain by ...
0
votes
3answers
119 views

Assuming $ f(x) = 1/\ln(x) $, plot $ \int f(x) \mathrm dx $ on (1, 5) [closed]

Assume $ f(x) = 1/\ln(x) $. Plot $ \int f(x) \mathrm dx $ on (1, 5) How can I make a plot even though $ x=1 $ could be zero in the denominator?