# Questions tagged [series-expansion]

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

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### Force Mathematica to display Series in factorial notation

The Series expansion for Sin[Pi * x] is Series[Sin[Pi * x], {x, 0, 10}] Pi * x - (Pi^3 * x^...
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### Series function not expanding an expression

I have the following code: FDE[d_, η_] := η^(d + 1)/Gamma[d + 2] + π^2/(6*Gamma[d])*η^(d - 1); Series[FDE[d/t, 1/η]/FDE[d/t - 1, 1/η], {η, 0, 3}] The series ...
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### Why doesn't Mathematica provide an answer while Wolfram|Alpha does, concerning a series convergence?

Among other series I've been working on, I was asked to find whether $$\sum_n 1-\cos(\frac{\pi}{n})$$ converged, and Mathematica's output to ...
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### How do I neglect suppressed terms in an expression?

I have an expression along the lines of expression = a^2 + a + b^2 + a*b Each variable has a big-O notation scaling, e.g. a ~ ...
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### Approximation of roots using Series

I am solving a fifth degree polynomial using Series. My equation looks like ...
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### Applying the command “expr/.rule”, to find the expansion of Cos[a+b]

how can i find the expansion of Cos[a+b], using the expression g[f[{a,b}]].So i am specified to use one shot replacement to get the expansion by replacing the argument of the expression given. I tried ...
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### Division by a series with no coefficients

I know it is strange, but it seems MA is unable to compute a simple series expansion ...
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### Evaluate parameters before function uses them

I want to construct a power series: LP[s_] := With[{x = 1, R = 10, n = 1}, Sum[cc[i + n, n, x, R] s^i, {i, 0, 20}]] but it kinda takes a long time to compute the ...
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### Pade approximation of vector or operator functions

PadeApproximant is a very useful function of MA that starts with a truncated Taylor series $$f(x)\approx\sum_{k=0}^{l} c_k (x-x_0)^k,$$ and represents them in a ...
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### Multivariate Lagrange inversion

I know that the function InverseSeries (Reference here) provides an interface for the Lagrange inversion formula. However I can't find anything on the ...
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### Bad Integral evaluation for Piecewise function

I have been trying to evaluate this symbolic function: f[ρ_, R_, α_, yp0_, yp_] := R*((ρ - R*Cos[α])^2 + (R*Sin[α])^2 + (yp-yp0)^2)^(-(1/2)); Mathematica can ...