# Tagged Questions

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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### Integrate yielding a ConditionalExpression but I don't think the condition is necessary

Suppose I take the PDF of the LogNormal distribution with parameters m and s evaluated at x. I obviously get an expression involving m. I now want to integrate that expression not with respect to x ...
332 views

### Integrate fails for generic parameters but works for any specific values (v. 10.0.x bug)

Bug introduced in 9.0 and fixed in 10.1 I was trying to get the following integral ...
343 views

### Riemann-Spherical Projection of Network onto the $\mathbb{R}^2$-Plane

I'm trying to find a way to plot the graph ...
303 views

### Can your Mathematica do the following integral?

Backslide introduced in v10 and fixed in v10.4.1. I was trying to do the following integral in Mathematica: Integrate[(z-2) PolyLog[2,z]Log[1-z]/z^3,z] What I ...
920 views

### Mathematica 10 cannot solve definite integral [duplicate]

Bug introduced in 10.0 and fixed in 10.0.2 Mathematica 10 fails to solve the following integral, saying that it does not converge. ...
343 views

95 views

### Inconsistent results for Integrate depending on irrelevant assumptions

I stumbled across this amusing issue today when doing some definite integrals: ...
426 views

### Conditional Expectation — How can Mathematica find a more general closed form?

Mathematica can't find a solution to this Expectation. ...
204 views

### Why should the spatial derivative order of the ODE *not* exceed two?

Following this question I came across this strange behaviour. Let me define a 1 D interval implicitely ...
192 views

### Differentiate the product of some terms

How can I compute the following derivative, $$\frac{\partial}{\partial \lambda_j} \prod_{i=1}^k (1+\lambda_i)e^{\lambda_i} \quad \text{for }\; 1\le j \le k$$ for some positive integer $k$ which is ...
311 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 ...
643 views

### Integrating over Bessel Function erroreous? (Hankel Transform)

Bug introduced in 8.0.4 or earlier and persists through 10.2. The Hankel Transform is given by Integrate[f[x] x BesselJ[0, x t], {x, 0, Infinity}] It is self-...
80 views

### When is RegionMeasure[ImplicitRegion[…]] faster than (N)Integrate[Boole[…]]?

I wanted to use Mathematica to compute areas and volumes of various implicitly defined regions, so I ran a simple test case using the unit circle: ...
191 views

### Incorrect evaluation for Thue-Morse signed harmonic series

I would like to evaluate $$s = 1 - \frac{1}{2} - \frac{1}{3} + \frac{1}{4} - \frac{1}{5} + \frac{1}{6}+\frac{1}{7}-\frac{1}{8} - ... + \frac{(-1)^{\textrm{binary digit sum}(n-1)}}{n} + ...$$ where ...
360 views

### How to do algebra on unevaluated integrals?

I am working with functions calculated from a set of general basis functions. ...
853 views

### Why does Mathematica spit this back out?

I'm struggling with the integral, $$\iint\sqrt{4a^2-x^2-y^2}dxdy$$ taken over the upper half disk of radius a centered at (a, 0). When I type it into Mathematica (10.2), Mathematica spits it back out....
307 views

### Derivative of contour in ContourPlot

Sorry to bring this question up again, since there are many similar questions on the site. I use to think this is a easy job to do, because for the worst case I can follow the answers on this site. ...
468 views

### Convolve does not get the correct answer

Convolve[Sinc[x], Exp[-x^2], x, X] (* E^-X^2 π *) is obviously false, but why? Any suggestions ?
237 views

### Limit of partial sums involving inverse squares

Consider the finite sum rs[x_, n_] := x/n Sum[n^2/(i + (n - i) x)^2, {i, 1, n}] Is there a way to bring Mathematica to calculate the limit for ...
1k views

### How to expand a function into a power series with negative powers?

Is there any way to expand this expression a+b(1-Exp[-T/(b c)]/(z-Exp[-T/ (b c)]) (where a, ...
388 views

### Integrate to calculate enclosed area

I am trying to 'use an integral in polar coordinates to calculate the area enclosed by this curve': The curve is: r=sin2θ, θ ∈ [0, π] which I believe is already in ...
2k views

### How to find the non-differentiable point(s) of a given continuous function?

For example, the non-differentiable point of the function $f(x)=|x|$ is at $x=0$. How to find the non-differentiable points of a continuous function that is defined numerically?
277 views

### Limit of Nested Radical $\sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+…}}}$

I want to find limit of infinite nested radical $\quad \quad \sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+...}}}$ but I don't know how to define this expression in Mathematica. How can I define it and ...
266 views

### Limit not giving expected result

I am taking the limit Limit[Sin[π Sqrt[4 n^2 + n]], n -> ∞] the returned answer is Interval[{-1, 1}] I think the right ...
369 views

### Force integration to be linear over sum?

Is there an obvious way to force Mathematica to separately integrate the terms in a sum? According to the docs, When part of a sum cannot be integrated explicitly, the whole sum will stay ...
397 views

### What is the mathematical meaning behind D[f]?

y = a + b x; I can understand this output of the ordinary differentiation of y w.r.t. x <...
438 views

### How do I compute the entropy of the beta distribution?

I tried Expectation[-q*Log[q], q \[Distributed] BetaDistribution[a, b]] and got ...
2k views

### Can I define a function for vectors of arbitrary dimension?

Is it possible to do analytic calculations with Mathematica? For example, I want to compute: $$\partial \frac{\sum_{j=1}^n G_{j} \prod_{k=1}^{j-1} (1 - G_{k})}{\partial G_l}=-\prod_{k\neq l} (G_k-1)$$...
247 views

### Curvature Application

I found these amazing animations at https://courses.engr.illinois.edu/tam212/avt.xhtml#avt which I think will be wonderfully useful when teaching multivariable calculus next semester. I've started to ...
530 views

### Lagrange Multiplier

We are asked to maximize and minimize $f(x,y)=4xy$, given the constraint $4x^2+y^2=8$, using the Lagrange Multiplier method. First, I enter the functions f and g. ...
376 views

### How to solve this probability symbolically or numerically?

I am trying to calculate the following probability $$\mathbb{P} \big(\sum_{i=1}^{m} (A_i + S_i) \le L < \sum_{i=1}^{m+1} (A_i + S_i) \big)$$ where, A_i \sim \exp(\lambda), \quad S_i \sim \exp(...
304 views

### An integral with a fractional part in 3 dimensions

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

### Animate the line integral over a scalar field

There is a gif from Wikipedia, The line integral over a scalar field $f$. How to plot and animate this in Mathematica?
215 views

### Speed up derivative evaluation

I'm trying to calculate the normal vectors and the tangent vectors at the discrete points of a suface. For example: ...
324 views

### Find exponential generating function from the first few terms

The function FindGeneratingFunction computes the ordinary generating function of a sequence, given a sufficient number of initial terms. I have two questions in ...
1k views

### Can't compute definite integral

Consider a scalar field (in polar co-ordinates), $f(r) = l-r$. Now I want to evaluate the field integral over a circular region of radius $b$, centered at a distance of $x$ from the origin. According ...
203 views

### Defining a function implicitly and calculating its derivatives

I'm interested in using Mathematica's symbolic manipulation to obtain, for a particular function $f$, derivatives of arbitrary order evaluated at zero. Normally I'd use the ...
193 views

### Series resulting in “No more memory available.”

Is there any way to force Mathematica to come up with the closed form to Sum[1/(i^18 (i^2 + j^2)), {i, 1, Infinity}, {j, 1, Infinity}] or ...
368 views

### Using Grad, Div, etc in polar coordinates

I'm trying to use the newish functions Grad and Div to work with a PDE with circular or spherical symmetry and getting what looks to me like a wrong result. However, I'm not sure of this--perhaps I ...
461 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 ...
302 views

### Traces of the level surface $z=4x^2+y^2$

I came up with this method to plot the traces of the surface $z=4x^2+y^2$, in this case for $z=1$, 2, 3, and 4. ...
210 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: ...
101 views

### Is it possible to find a function from first few terms in the expansion

Is it possible to find a function if first few terms of the expansion is known. For example if I have this series \$f(x)=\frac{k^3 x^2}{6}-\frac{k^5 x^4}{120}+\frac{k^7 x^6}{5040}-\frac{k^9 x^8}{...
1k views

### Convolving/integrating problems

Let's say I want to convolve two functions (f and g), a gaussian with a breit-wigner: ...
153 views

### Strange DiracDelta integration results in 10.4.1

Integrate[DiracDelta[s (x - c)] x, {x, -Infinity, Infinity}, Assumptions -> {s > 0, c > 0}] gives me c/s in ...