Linked Questions

5
votes
2answers
254 views

Series expansion of a multivariable function to an order n for any number of variables [duplicate]

Suppose I want to expand a multivariable function to an order n. ...
0
votes
2answers
399 views

Asymptotic series [duplicate]

I need to solve the following problem. I have the following function: Erf[Sqrt[a x^2 + b y^2]]/Sqrt[a x^2 + b y^2], where x and y are variables and a and b ...
0
votes
1answer
467 views

Two Variable First Order Approximation [duplicate]

I found that using Series and Normal command, I am able to approximate the first order of x or y, but If I also get rid of x*y (cross term), Series command does not work any more. Let's define some ...
1
vote
1answer
137 views

Multivariables series expansion up to some power of all the variables [duplicate]

I have a function f[x, y, z] that I would like to expand up to a given power of xyz. For now, I am using ...
1
vote
0answers
118 views

Best way to power series expand in multiple variables? [duplicate]

A power series expansion of a multivariate function can be performed with the Series command, which performs each expansion consecutively. The results can be a bit ...
0
votes
0answers
67 views

Speed up series expansion [duplicate]

I have a rather complicated function that I need to expand it in series, which is quite straightforward but takes a long time. I was wondering if there is a way to speed up such a calculation: ...
0
votes
0answers
18 views

Truncate Multivariate Polynomial to Degree [duplicate]

I am working with multivariate polynomials, e.g. Expand[Normal[Series[d/Sqrt[(1 - x^2 + y^2)], {x, 0, 5}, {y, 0, 5}]]] which for this example results in $\frac{...
5
votes
3answers
324 views

Get the homogeneous part of a polynomial

What is the easiest or fastest way to extract the homogeneous part of a polynomial in Mathematica. For instance, if there were a function homog_part[f,n], I could ...
3
votes
4answers
2k views

Calculating Taylor polynomial of an implicit function given by an equation

I'd like to write a procedure that will take an equation: F(x,y,z) = 0 chosen variable: x a point: ...
7
votes
1answer
682 views

Series expansion for small ratio of variables

I have a messy expression of variables that I would like to simplify under the assumption that certain ratios of the variables are small. For example, consider $\sqrt{x+y}\;$ expanded for small $\...
2
votes
3answers
499 views

Choosing a branch of the square root when performing a series expansion

I have the following problem. Consider expression f=Sqrt[(x-2y)^2] There is an obvious ambiguity in the definition of f ...
6
votes
1answer
282 views

Successive Series Expansion Bug (?)

I've found what appears to be a bug in MMA related to taking successive series expansions. I'm providing this minimal example and post as other posts didn't appear to address the issue I found. In ...
3
votes
3answers
194 views

Construct approximation by eliminating algebraic terms of small magnitude

Let's suppose that for the following expression: $\qquad \alpha\,\beta +\alpha+\beta$ I know that $\alpha$ and $\beta$ are of small magnitude (e.g., 0 < $\alpha$ < 0.02 and 0 < $\beta$ < ...
0
votes
1answer
557 views

Multivariate series expansions to different powers

I have a function that (I believe) correctly takes the multivariate Taylor series expansion about the origin for some expression (first argument), in some variables (second argument, list), to ...
4
votes
1answer
106 views

Pertubation series of given equations

I would like to define a function that does the following. If I have an equation, for example: $$f(x)+[1-f^2(x)]+f^{\prime\prime}(x)+f(x)\ f^\prime(x)=0$$ and I am given a value for $f$ to expand ...

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