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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Calculate the expectation of psi(x) with a gamma density x∼Gamma(α,β ) [migrated]

Suppose I have a Gamma distributed random Variable x∼Gamma(α,β). Now I want to calculate the following expectation values (integrals): E[psi(x)] with psi(x) being the digamma function Many thanks ...
0
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0answers
9 views

One point following another moving in a straight line? [migrated]

There is a plane with two points on it, let's say A and B. A starts at an arbitrary constant point, let's say (0, 0), and B at a point that needs to be tested, which we'll call (c, d). A moves ...
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1answer
49 views
0
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0answers
38 views

Solve defined integration problem [on hold]

How can the following be solved for ln(L_i/L_f) ? Limits are in good place in this problem. ...
0
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0answers
35 views

Integration problem: lrgexp

I want to calculate the following integration but it gives the error PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD. The code is: ...
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2answers
49 views

Derivative of Continuous and Differentiable Piecewise function is indeterminate

I'm attempting to analytically stitch together two linear functions with two quadratic functions. The function I'm considering, then, is a piecewise function consisting of 4 parts. Below are the ...
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0answers
51 views
2
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0answers
40 views

Computing an inexact derivative with some terms preserved in exact form

I am beginning to learn Mathematica and have the following question: How can I return a derivative with exact numbers instead of one involving numerical approximations? My original, single variable ...
1
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1answer
92 views

Integral equation

I'm trying to solve the following integral equation: Integrate[-k/2 Exp[-k Abs[x-z]] f[x], {x,0,d}] == a f[z] Differentiating twice with respect to z should ...
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0answers
26 views

Multivariable Integrate [on hold]

Why won't Integrate[r^3, {r, 0, a - a/b z}, {z, 0, b}] work? The integral symbol method works though:
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1answer
98 views

Limit of a fractional integral

I am trying to find the limit for λ -> 0 of the integral listed below, but Mathematica give me only a ConditionalExpression ...
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0answers
55 views

Asymptotic forms of Bessel function

I want to replace Bessel functions by asymptotic forms, so the question is: can I find the best ones with help of Mathematica? And if it's possible, how can I do it? Update How can I get with ...
2
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0answers
35 views

Does DynamicModule cure Problem with Manipulate?

Hopefully, this is a final cure for the Problem with Manipulate introduced on A problem with Manipulate and then continued on Continuation of a Problem with Manipulate. Michael E2 suggested on the ...
6
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3answers
154 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: ...
1
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0answers
72 views

How can I improve the solution of my PDE?

I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
1
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1answer
52 views

Continuation of a Problem with Manipulate

For the beginning of this discussion, see: A problem with Manipulate. Now, the final use of the Initialization command doesn't protect the Global workspace. What I am discussing is not a single ...
-2
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1answer
112 views

Mathematica's steps towards the result of a definite integral

I am interested in this definite integral: $$ \eqalign{\int_0^\infty {x^2 \log(1-e^{-x})}\; dx\cr } $$ That is: ...
0
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0answers
91 views
4
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3answers
349 views
0
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0answers
54 views

Bug (?) in Mathematica in Derivative of function with Abs [duplicate]

I encountered a weird problem with Derivatives in Mathematica, see the following code: ...
0
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1answer
83 views

Numerical integral speed

I have the following code to calculate a numerical integral for any given a, however it takes a very long time, even with adaptivemontecarlo, which is not accurate enough: ...
18
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4answers
776 views

A bug in Integrate

Integrate[(1 + 16 Tan[2 x - y]^2)/(1 + 4 Tan[2 x - y]^2), {x, 0, 2 π}] Mathematica (wrong) output is (tested under versions 8 and 10.0, took ~ 1 minute of CPU ...
2
votes
1answer
94 views

Missing zero in the CoefficientList

The following list has a length only 10 (not 11) CoefficientList[Series[ArcTan[x]/(1-x^2),{x,0,10}],x] {0, 1, 0, 2/3, 0, 13/15, 0, 76/105, 0, 263/315} It should ...
5
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0answers
114 views

Wrong Limit in Mathematica 10.0.0

Limit[(Log[(3+Sqrt[5])/2]/(2*Log[(1+Sqrt[5])/2]))^(-1-2*n), n -> Infinity] Mathematica (wrong) output: 0 But this is ...
5
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0answers
117 views

Wrong Limit with LaguerreL

Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞] Mathematica (wrong) output ...
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0answers
62 views

convergence problem - triple integral

I have a problem in convergence ... for i=j=5 is enough to calculate what i want. But for os11[100,5,5]=1.59 ( 1.58 is the real ...
4
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2answers
121 views

definite integration very slow

I have to perform definite integration of function of this kind : ...
5
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0answers
63 views

LogisticSigmoid residue bug?

On version 10.0 for arm: Residue[LogisticSigmoid[z],{z,I Pi}] gives 0 not 1. Can anyone reproduce this?
2
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1answer
148 views

How to speed up a symbolic integration

I have a question about an integral. I wanna integrate this: ...
7
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2answers
210 views

Why does Mathematica say $\int_0^1\int_0^1\int_0^1\frac{1.0}{xyz}\,dz\,dy\,dx=0$?

Mathematica 9 says that $\int_0^1\int_0^1\int_0^1\frac{1.0}{xyz}\,dz\,dy\,dx=0$ and $\int_0^1\int_0^1\int_0^1\frac{1}{xyz}\,dz\,dy\,dx=0$. ...
0
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1answer
46 views

Problem with 'time dependent' functions [closed]

I'm just trying to make $\frac{dx}{dt}$ where $x= \rho \cos\theta \sin\phi$ where $\theta, \phi $ and $\rho$ are time dependent functions. ...
5
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1answer
182 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 ...
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0answers
42 views

Multidimensional integration does not work

I am trying to solve an integral over Cubic Birillioun Zone, but after taking a long time Mathematica give nothing in return and just repeating the integral form, here is my integral, ...
0
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1answer
35 views

Plotting partial sums of Taylor Function

I need to plot the partial function: $T_f(x)=\log 2+\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{2^kk}(x-2)^k$ for $n=2$,$n=4$ and $n=6$ on the same plot over the interval $[-\frac{1}{2},4]$ and also the ...
-2
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1answer
46 views

Need help to solve this math question when x reach 0 [closed]

My son can home and ask me to help him with this equation: lim ((x-2)/(2x-1))^(1/x) x→0 I try to use /www.symbolab.com but its too complicated to solve this. Thanks with the help
2
votes
1answer
166 views

How can I evaluate surface integral in Mathematica?

$$\iint_{S^+}x^3dydz $$where $S$ bottom part of $$ \frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$$ $S^+$ - outer side of $S$ $$\iint_{S^+}P(x,y,z)dydz = \iint_{S}P\cos\alpha dS,\ \; normal : ...
0
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0answers
33 views

Series Expansion of Differential Operators [duplicate]

We know about the possibility of series expansion of a function in Mathematica. Same as below, where a function f[a x] is expanded around zero up to 5th order. ...
0
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0answers
45 views

Integration is unevaluated analytically after a variable removed

I am using Mathematica 9.0 to do a symbolic integration as follows: ...
3
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0answers
40 views

Indeterminate expression 0(I*Infinity]) on indefinite integrals on first use only

I do not know if this is new or not, I googled before. Windows 7, 10.1 64 bit: Integrals generate this error message The strange thing also is that the message shows up the first time the command ...
3
votes
3answers
93 views

Factoring a separable integral with a product of independent integrands

I would like to input someFunction[Integrate[p[x] p[y], {x, -1, 1}, {y, -1, 1}]] and to get the following output ...
4
votes
2answers
65 views

Inconsistent Integration involving DiracDelta at boundaries

I'm working on integrals involving DiracDelta functions at the boundary of the integrals. I'm confused by the output Mathematica v10.1.0 gives me in this case: ...
8
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5answers
665 views
0
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2answers
60 views

Continuity of function-example

I'd like to examine the continuity of the following function: f[x_] := Limit[(n^x - n^(-x) ) / (n^x + n^(-x) ), n -> Infinity] I know that this function isn't ...
7
votes
1answer
143 views

Curious solutions of x' = Sqrt(x), x(0)=4

Consider the solution of $x'=\sqrt{x}$, $x(0)=4$ using DSolve. ...
5
votes
1answer
56 views

Integrate gives Simplify::infd “simplified to Indeterminate” message

Using version 10.1 on windows 7 Integrate gives this Simplify::infd Kernel message. What causes it, is this a bug? ...
1
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2answers
83 views

Plotting a function based of a complicated integral

I would like to have help in making a plot of a complicated function based a definite integral. - desired graph My calculation: ...
3
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0answers
79 views

DiracDelta and version 10.0.0

Note: This issue seems to affect version 10.0.0 only and is fixed in 10.0.1, 10.0.2, and 10.1 When evaluating the following two inputs: ...
0
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0answers
44 views

Is there a way for me to get Mathematica show its steps? [duplicate]

I have seen similar questions but they were quite dated (3+ years). When performing, say an Integration, it would be beneficial to see the major steps such as variable substitution, change the order ...
0
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1answer
55 views

Using Assumptions in Expressions that Evaluate to be Elliptic Integrals

I have the following integral that I am trying to evaluate in Mathematica: $\int \sqrt{\alpha + m g l \cos(q)} dq$. If $\alpha > m g l$, then the result is a complete elliptic integral of the ...
0
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3answers
83 views

Revolution of two curves around the y-axis

I've looked through the other posts on rotating a function around the x or y axis and haven't had any luck. my question is this how do i rotate the area between the functions $f(x)=x^2+1$, and ...