# Questions tagged [series-expansion]

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

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### Perturbing a tensorial expression

I am new to Mathematica. I am trying to simplify an expression of the some form like: $$n_i \sigma_{ij} n_j - \gamma n_i \hat{\sigma_{ij}} n_j = 2 + v_i x_i + \kappa E_{ij} \chi_{ji}$$ There are ...
203 views

### Can Mathematica simplify an ordinary differential equation (ODE) by assuming a power series solution and obtain the recurrence relation?

I have an ordinary differential equation and want to solve it using power series as ψ[x_] = Sum[Subscript[a, n] x^n, {n, 0, ∞}] to obtain the recurrence relation ...
51 views

233 views

### Using Integrate and then Series seem to produce a wrong result

Bug introduced in 11.1.0.0 or earlier and persisting through 14.0 or later Run this: ...
1 vote
93 views

### Limit of Hypergeometric Functions

Mathematica (12) seems to have a lot of trouble with taking limits involving hypergeometric functions. A simple example I am interested in is the following ...
57 views

### Series behavior for self-defined function

How to make Series give the correct expansion of a self-defined function? For example, for some reason, I use f[x] to represent ...
132 views

### Asymptotic solution of a system of ODEs

I have the following system of Ordinary Differential Equations (ODEs) together with initial values ...
1 vote
67 views

### Expanding polynomials using valuation

I would like to expand the polynomial $p(\lambda) = \sum_{i=0}^{d} a_{i} \lambda^{i}$, as $F(p(\lambda), \lambda_{0})= \min_{j} [ val(a_{j}) + j \lambda_{0} ]$ with $\lambda_{0}$ being a real ...
1 vote
117 views

### How can I fully simplify sum that includes absolute value?

Consider the following sum: ...
181 views

1 vote
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### How to accelerate Inverse[] for positive definite matrices symbolically?

I am trying to construct a positive definite matrix based on the multiquadric radial basis function (RBF) for a set of thirteen points symbolically in order to later approximate the Laplacian operator ...
117 views

### Why AsymptoticSolve` doesn't work for a multivariate implicit function?

I started by defining ...
34 views

### Attempt to evaluate a series returning Indeterminate while running Plot

I have a function in the form of a Series from a prior calculation: sol2D = SeriesData[a, 0, {Rational[3, 16] Pi, Rational[-5, 2], Rational[3, 4] Pi}, 0, 3, 2] ...
257 views

### Possible error with series expansion

I'm expanding the following expression around x=1 ...
1 vote