Questions tagged [calculus-and-analysis]

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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53 views

Limit of a complex function of a complex variable expressed in polar form

I've got the complex function $$f(t;z,\mu) = \mathrm{e}^{-z\sinh t-\mu t}$$ where $$t=R \mathrm{e}^{i\theta},\theta \in [0,\pi/2]$$ The function depends on two parameters, $$z>0, \mu \in \mathbf{C}$...
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1answer
53 views

Can't extend the function to continuous

I have code: Am0[ω_] := Abs[H[I*ω]] Am[ω_] := Piecewise[{{Limit[Am0[ω], ω -> 0], ω == 0}, {Am0[ω], ω!= 0}}] Limit[Am0[ω], ω -> 0] Am[0] Function ...
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1answer
161 views

Is this a bug in mathematica for integrals of multiple error functions?

I'm scratching my head over the the following result in Mathematica (v11.3) I'm considering the function B = Erfc[x] Exp[-x^2/2] + Sqrt[2] Erfc[x/Sqrt[2]] Exp[-x^2] ...
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1answer
387 views

Three Dimensional Plot of Numerical Integral with Delta Function

I want to plot the definite integral of the following function ...
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2answers
1k views

Change integration variable

Are there any automated procedures to change integration variables? For example by changing Sin[u]->x, I can change ...
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48 views

Problems with the output of the integral function

I write here because I've some problems when I want to integrate this quantity with respect to z: rH, a and z are real values, being TT4 a real value too and I especify that in the assumptions of the ...
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0answers
53 views

Problems with the function Integral [closed]

I write here because I've some problems when I want to integrate this quantity with respect to z: rH, a and z are real values, being TT4 a real value too and I especify that in the assumptions of the ...
2
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1answer
174 views

(Numerical) calculation of nested integrals

The problem I'd like to (numerically) compute nested integrals of the type $$I(a;k) \equiv \left( \prod_{i=1}^k \int_0^\infty \mathrm{d}x_i \right) \exp \left( - \frac{1}{4a} \sum_{i=1}^k \left( x_i - ...
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2answers
61 views

Lattices sums and Madelung Constant

the following sum represent Madelung constant of ionic crystal is not converget but it is possible to sum by different method, the sum is symetric for interger positive and negative so then $$\sum _{...
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3answers
289 views

How to find nth log derivative using mathematica?

Now I have a function, say $f(k,z)=e^{-kz}(1+kz)$ I want to find the $n$th $\log$ derivative with respect to z. like $(z\partial_z)^{(n)}f(k,z)$ (or $(\partial_{\ln z})^{(n)}f(k,z)$ if you like), ...
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1answer
65 views

How can I change the dependent variables of a function?

What I want is to define a function which depends of some variables and then get the expression for that same function when it depends of different variables. My specific case is: (where ...
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1answer
62 views

how to transform a decimal into a radical equivalent with minimal error,and find a correct syntax?

I have been solving this equation x^x^x == 36 , Mathematica does not give me a solution by applying traditional methods , neither with ...
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1answer
27 views

Numerical derivative (ND) not working for orthonormalized eigenvectors of a matrix

I have problem making ND work. Define relevant needs and vectors ...
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1answer
83 views

Accurate Numerical values of a given functional

Consider the following functional : $$ I(x,s) =\int_0^\infty\mathrm dy \frac{F(x + \mathrm iy, s) − F(x −\mathrm iy, s)}{\mathrm e^{2πy}-1}, $$ where $ F(z, s) = \dfrac{\sin^2[π\Gamma(z)/(2z)]}{z^s} $....
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Algorithmically imposing a substitution in a difficult integral

Consider the following integral: $$I = \frac{1}{\pi c^2} \int\limits_{r=0}^c 2 \pi r\ e^{-\frac{ \left( \sqrt{a^2 - r^2} -\sqrt{b^2 - r^2} \right)}{\lambda}}\ dr$$ under the conditions $a>b>c>...
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Madelung Constant [closed]

I would like to clarify some sums that being divergent can be calculated by different methods, but I find discrepancies with calculations with certain series already calculated xExamples $$M=\sum _{m=...
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1answer
43 views

NDSolve with embedded piecewise function for state-variable

Given ODE: $\dot{x}=-2 e^{-x^2} x + U$ where: $U=-u_{as}$ $u_{as} = \begin{cases} \frac{e}{\psi_+-e}, & \mbox{if } e\mbox{>=0} \\ \frac{e}{e-\psi_-}, & \mbox{if } e\mbox{<0} \end{cases}$ ...
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3answers
657 views

Exact Differentials

I just started using Mathematica so my apologies if this is a very basic question. I tried to find related questions on this forum but couldn't, so here goes. I have an equation, $\quad \quad dp =\...
2
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1answer
66 views

How to find the integrand by fitting data - spectrum reconstruction

Problem statement I have some experimental data of measurement values vs. temperature. Now, I want to find the spectrum which causes the measured temperature dependence. The measurement values are the ...
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0answers
50 views

Command to find the pre-image of a set that is mapped to by the function $f(x)=3^x \mod{17}$

$$f(x)=3^x \mod{17}$$ How to find the pre-image of the set if this function maps from real numbers to real numbers. What command would I use, to see the pre-image if the function would map from ...
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1answer
130 views

Help with an integral

I want to know if the following integral can be evaluated in Mathematica: $$ g(t)= c\int_{0}^{1-t} t^{m-1}\left[(u+t)^{m}-u^{m}\right]^{n-2}(u+t)^{m-1} d u$$ where $$ c= m^2n(n-1)$$ ...
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0answers
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Why is the convergent product with GoldenRatio evaluated as ComplexInfinity?

It is true that the following product has a singularity for k = 1, but from k = 2 it is convergent. We can be convinced of this by numerical calculation: ...
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1answer
47 views

Complex infinity with integration

In trying to compute following integral (spherical coordinates): $$\int[\rho+p_r]4\pi r^2dr$$ With:$$\rho=\frac{1}{2} f_0 \left(\frac{\sqrt{b_0 r}}{r^2 \sqrt{r \sqrt{b_0 r}}}\right){}^n$$ $$p_r=\frac{...
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1answer
39 views

I have a list of coefficients and I am trying to make a power series. How?

I noticed the Series[] command that would be perfect for Taylor polynomials. Unfortunately, I do not have the function available. I just have a list with the ...
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1answer
52 views

Double integral with a variable in limits

I am trying to solve this integral: This is what I tried: ...
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0answers
115 views

Evaluating a 2d integral

I would like to calculate this integral \begin{align*} I(s_1,s_2,s_{12},m) = \int_{0}^{1} {\rm d}x \int_{0}^{1-x} {\rm d}y \Big( x y \Big[ y(1-y)s_1 + x(1-x)s_2 + 2 xy s_{12} -m^2 \Big]^{-1} \Big), \...
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1answer
86 views

How to show the resulting function hidden by Mathematica?

I have u0[r_, phi_] := Sum[I^(-n) BesselJ[n, r] Exp[I n phi], {n, -n, n}]; Limit[u0[r, phi], n -> Infinity] but the result is not exportable to TEX, as it is ...
18
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3answers
630 views

Heuristics, tricks, and hacks in symbolic math

Mathematica sometimes fails to compute symbolic solutions when posed in the direct or obvious code, but succeeds when the same fundamental problem is posed in a slightly different way, or when ...
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0answers
85 views

Why can't Mathematica integrate my function?

I am very new to Mathematica and have been trying to integrate a function p[f] that is expressed as follows ...
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2answers
90 views

How to integrate faster [closed]

I always wanted to know how to speed up my integral computation in Mathematica. Is there some techniques that i am unaware to make the integration faster. Here an example: ...
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1answer
58 views

Function that accepts functions and returns an expression containing their partial derivatives

I would like create a function that takes functions as input and includes different partial derivatives of the input functions, for simplicity's sake say: $\qquad m(f(x,y),g(x,y))=f_{xxx}(x,y)+g_{xyy}(...
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1answer
87 views

Question about forcing derivatives

I'm here with another probably simple question. So I am taking derivatives of a function with respect to another variable not used in that function. So first I define that derivative ...
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1answer
43 views

EllipticPi argument is complex and can not be plotted. How to handle this problem?

inttau[r_]=-(1/Sqrt[0.0345106153943703 - ((37.3042 - r) (-25.578 + r) (62.8822 + r))/(3000 r)]) This is my function of r, now I integrated it w r t r ...
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1answer
436 views

How to Mellin transform a complicated Log integrand?

I got a question concerning an integral. I need to know the analytical expression. I have to Mellin transforn a function and the integral is then sth. like this: $$ \int x^{N-1} \frac{Ln(a -x)}{1-x} ...
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1answer
46 views

Integration taking too long

Mathematica is having issues with the following code: ...
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1answer
67 views

How to make traditional output of derivatives display like an equation

I was following a code given by Jens in the following Question and I want to improve the way my equation is displayed. The current code I'm using: ...
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3answers
62 views

How to ask Mathematica to do the given operation for a set of parameters?

I have a set of numbers like this s = {a, b, c, d, e, f, ..., g, h} and I would like to ask Mathematica to do the following operation (to sum the subtractions of ...
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2answers
60 views

Something does not work when minimizing a function

So basically I am trying to minimizing a function. I use the command "FindMinimum" since "Minimize" just returns the input. FindMinimum gives me the minimized potential and the ...
1
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1answer
67 views

How to assign values of variables with index

I'm trying to plot the following function $V(\{r_j\})=\sum^n_{i<j,j=1} \frac{1}{|r_i-r_j|^2}$ in Mathematica. For the expression of this function, I wrote ...
5
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1answer
464 views

Integral of DiracDelta giving an unusual answer

I have been getting a number of seemingly inconsistent solutions to integrals of Dirac delta functions in which the integrand evaluates to DiracDelta[0] at one of ...
2
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1answer
130 views

Problems with improper integrals in higher dimensions

Calculating numerically certain energy integrals in three and four dimensions related to the Riesz potential and the capacity, I try ...
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1answer
76 views

How do I plot the derivative of the Cantor Staircase?

I know that the derivative of the Cantor Staircase should be close to 0 since the Cantor Set has a measure of zero. I wanted to graph the derivative of Cantor's Staircase in Mathematica to see if it ...
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1answer
30 views

Search for terms contatining error functions

question might have an answer in this post (Efficient Search for specific Terms in symbolic Expression) but i don't understand how to convert it to my specific case Through some definite integrals I ...
3
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0answers
96 views

Summation variables aren't recognised as dummy variables

I'm trying to write this expression in Mathematica, and calculate the following quantity However, when I tried the following ...
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0answers
66 views

Why are the numerical and analytical evaluation of this integral not the same?

Since my integral and the way I used to solve it was so long, I put a .nb file here including all data which are needed. You can use it to try my question after reading the following details I had ...
18
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3answers
3k views

Is there a built-in function which detects singularities in a function?

Given a function f[x] and a region M in the complex x-plane, how can I find singularities of f in this region, i.e., issue a ...
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1answer
45 views

Partial derivative on a Solve solution

Trying to solve a demand-supply equilibrium here and them find a partial derivative of the equilibrium with respect to the parameters. ...
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1answer
95 views

Fitting an integral function given a set of data points

I have a set of measures of the resistivity of a given material at different thicknesses and I'm trying to fit them using the Fuchs-Sondheimer model. My code is: ...

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