Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].

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10
votes
1answer
337 views

Limit of sequence of functions behaving strange

I'm trying to determine the limit of the sequence of functions $$f_n(x)=\left(\frac{1}{\pi}\arctan(n x) + 1/2\right)^n. $$ I define ...
0
votes
1answer
42 views

DSolve with coefficients and assumptions

The command below: DSolve[{s'[t] == l t, s[0] == 0}, {s[t]}, {t, 0, a}] gives the error DSolve::alliv: The function <...
11
votes
0answers
300 views

Simplify and Sqrt, inconsistent behavior?

I have encountered some problems when using Simplify with expressions containing a square root and isolated a following test case ...
7
votes
0answers
81 views

Need explanation on strange behavior of Simplify under given assumption

This is quite surprising to me. Simplify[a == b, {a == {1}, b == {1}}] a == b does not evaluate the equality, while <...
5
votes
0answers
53 views

External and internal Assumptions on `PiecewiseExpand` and `Mod`

After this question I'm intrigued about the different behaviors depending where and how the assumptions are given. ...
5
votes
0answers
64 views

SumConvergence fails in version 10

SumConvergence[(-1)^(n + 1) ((Cos[n^2] + Sin[n + 2])/7^n), n] Mathematica fails to provide a result (true/false) but wolfram alpha works. What should I do ? It ...
5
votes
0answers
141 views

Calculating a limit with a result that is discontinuous in the parameters

The following limit is left unevaluated (Edit: added the assumption that $\epsilon$ is real thanks to the comment below): ...
4
votes
0answers
107 views

Multiple Constrained Sum

I need to perform a multiple summation, that obeys some conditions. This arises in the study of a statistical physics model. q=Exp[-β]. I would like to ask if ...
3
votes
0answers
78 views

Why isn't Mathematica listening to my assumptions?

I'm trying to simplify the expression ωplus := 1/2 c (I f V + Sqrt[4 k^2 - f (f + 8 I k) V^2]) so that I can get it in the form $a+i b$. I am using the global ...
3
votes
0answers
146 views

Assuming monotonicity and concavity

I have an expression that I would like to evaluate: 2 phi''[1 + a (-1 + u[10])] phi'[q]^3 > phi''[q] phi'[q] phi'[1 + a (-1 + u[10])]^2 Is there any way of ...
2
votes
0answers
94 views

How do I apply assumptions to a module (or any CompoundExpression)?

Edit: I am looking for a way to apply assumptions to all expressions contained in a compound expression. For example, ...
2
votes
0answers
246 views

Computing a sum

I'm trying to make Mathematica compute this sum: Sum[(-1)^k (n - k)^2 Binomial[2 n, k], {k, 0, n}] As is, I get an awful formula: ...
2
votes
0answers
707 views

I can't solve this set of equations

I am having trouble solving a set of equations using Mathematica 8. I do not get any errors, but I don't get any solutions either. My parameters and variables are real and non-negative. ...
1
vote
0answers
60 views

Assumptions aren't working in this sum

I have a sum that should be real: FullSimplify@Sum[1/(α n^4 + β), {n, 1, ∞}, Assumptions -> α > 0 && β > 0] But the result have involved even ...
1
vote
0answers
101 views

Assumptions don't work as expected in FourierTransform

The 2D rectangular function and its Fourier Transform is $$ g_{in}(x,\,y) = rect(\frac{x}{x0}) \, rect(\frac{y}{y0}) \quad \xrightarrow{\mathscr{F}} \quad G_{in}(u,v) = x0 \, y0 \, sinc(\pi u x0) \, ...
1
vote
0answers
114 views

How can I force the assumption that a symbol is a vector of n zeros

Using $Assumptions = Element[n, Integers] && Element[a, Vectors[n, Reals]] I can assume that a is a n-dimensional vector of Reals. How can I assume that ...
1
vote
0answers
135 views

Piecewise functions Integration with symbol

I want to integrate one piecewise functions as following, ...
1
vote
0answers
80 views

Getting long complex-valued integrals when simpler real-valued expressions exist

I have a long list of real-valued functions I'd like to integrate symbolically. For many of them, Mathematica gives me results with long complex-valued expressions involving weird functions such as <...
1
vote
0answers
86 views

How does TensorReduce use assumptions?

I would like to use TensorReduce by assuming that certain patterns of functions are tensors. From documentation of TensorReduce: ...
0
votes
0answers
43 views

Impose conditions on differential equations

This is my first post in Mathematica Stack Exchange, so thanks for your help and sorry for any rookie mistakes. I am solving the Einstein equations for two vectorial pertubations h_Alpha and v_Alpha ...
0
votes
0answers
30 views

Finding parameters that give constrained eigenvalues of matrix

I want to obtain the eigenvalues $x_1,x_2,x_3$ of a hermitian, off-diagonal matrix, {{0, Conjugate[d], Conjugate[g]}, {d, 0, Conjugate[h]}, {g, h, 0}}, under the ...
0
votes
0answers
50 views

vector with conditions/assumptions

Probably I just don't get it and it is because it's friday morning. I want to create a systems description fSys = {{x2}, {u g[x] + h[x]}}; However, there is a ...
0
votes
0answers
113 views

Using assumptions when calling Simplify from Collect

I am quite new to Mathematica, so please be patient ;) I have a very long equation that I have to sort for powers of a variable called e and that I want to ...