Questions on dealing with series data and constructing power series expansions of functions.

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9
votes
3answers
2k views

Multivariable Taylor expansion does not work as expected

The basic multivariable Taylor expansion formula around a point is as follows: $$ f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot ...
9
votes
1answer
513 views

How does Mathematica understand branchcuts of the complex logarithm?

Say I have the function $f(x) = x \tanh(\pi x) \log (x^2 +a^2)$ where $a$ is some positive real number. Then it seems to be me that Mathematica when given such a ...
9
votes
2answers
492 views

Find closed form expression for series expansion coefficients [duplicate]

Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function? Series will only give the explicit ...
6
votes
1answer
719 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, ...
8
votes
1answer
1k views

Solving an ODE in power series

How do I find a series solution to an ODE? I do not mean taking the Taylor series of an exact solution; I want to solve nasty nonlinear differential equations locally via plug and chug. Surely, that ...
3
votes
3answers
424 views

Limiting form of a polynomial expression

When simplifying an expression by hand, a trick that is often used is to remove terms that are lower powers of the independent variable, for instance, as $x \rightarrow \infty$, $x^2 + x$ becomes ...
1
vote
1answer
519 views

How can I get a Taylor expansion of the Sin[x] function?

How can I get a Taylor expansion of the Sin[x] function by the power series?
3
votes
3answers
177 views

What is the formula for this numerical series?

I'm developing a questions game. My goal is that the score for each correct answer will increase as the user answers more questions. Initially there are 15 points for each correct answer. Every 4 ...
10
votes
1answer
259 views

Why does Mathematica fail to series expand this simple expression?

I wanted to expand the function $(x+2)^{x+2}$ around $x = -1$, that is, using Series[(x + 2)^(x + 2), {x, -1, 2}] and Mathematica returns the same expression. ...
4
votes
1answer
237 views

Erfi[z] expansion in Mathematica: is this a bug?

Looking at the expansion: Series[Erfi[x], {x, Infinity, 1}] I obtain -I+E^x^2 (1/(Sqrt[\[Pi]] x)+O[1/x]^2) (note the ...
4
votes
2answers
465 views

How do I solve N simultaneous equations for N variables?

I have a function: f[x_] := x + 31 x^3 + 5 x^25 Which I want to find an expansion for: ...
12
votes
4answers
781 views

Evaluation of a triple sum does not finish in reasonable time

I'm trying to compute the following triple sum, but no result is produced within a reasonable amount of time. What to do? ...
5
votes
1answer
112 views

Apparently contradictory output from Series and D

I defined a function as: g[b_] := Integrate[f[n]Exp[-b DA (n.u)^2], n] Obviously D[g[b], b] /. b -> 0 gives ...
4
votes
1answer
155 views

List manipulation - various

Update OK, Please forgive the messiness of this, but I am working with something like: ...
3
votes
4answers
142 views

Exponential of a Differential Operator

In Mathematica, is it possible to exponentiate a differential operator such that the operator will act on a function, $f(x,p)$? Specifically, I wondering if I can get Mathematica to do this: ...
3
votes
2answers
119 views

Change all values of a series to positive values

I would like to change all values of a series to positive values. I refer to my previous question, answered in the most part, very elegantly by RunnyKine. However, there remains a slight glitch that ...
2
votes
2answers
664 views

About generating power series

For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows, ...
0
votes
1answer
57 views

nested series expansion

I have to invert the following matrix in which the functions U[t,x,y,r] and K[t,x,y,r] and all their derivatives are "small"; ...
0
votes
1answer
89 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 ...