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### 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. ...
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 ...
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 ...
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 ...
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 ...
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: ...
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### 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 ...
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 ...
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 < $\beta$ < ...
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 ...