# Tagged Questions

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

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### 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 ...
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### How to force Series[] to compute expansions by considering non commutative multiplication?

I wish to compute the Taylor series expansion of the following iteration method $x_{k+1}=x_k-f'(x_k)^{-1}f(x_k)$ up to four terms of error ($e_k=x_k-\alpha$). When this is a scalar iteration, I very ...
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### 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? ...
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### 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. ...
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Is it possible to find a function if first few terms of the expansion is known. For example if I have this series $f(x)=\frac{k^3 x^2}{6}-\frac{k^5 x^4}{120}+\frac{k^7 x^6}{5040}-\frac{k^9 x^8}{... 1answer 479 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 ... 2answers 726 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: ... 2answers 161 views ### How to get Series to recognize user-defined function has pole Edit for clarity: How does Mathematica's function Series know that Gamma[x] has a pole at ... 1answer 117 views ### Changing default behavior of Series to give slightly different SeriesData I am working with complicated expressions expr that contains the symbolic function f[x] which I know to have a pole at ... 1answer 297 views ### Dirichlet coefficients as limits: wrong Perhaps I should have included the word "bug" in my question. Here we go There is a bug in this Limit Limit[3^s (-1 - 2^-s + Zeta[s]), s -> ∞] (* 0 *) which ... 1answer 119 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 ... 1answer 186 views ### List manipulation - various Update OK, Please forgive the messiness of this, but I am working with something like: ... 3answers 172 views ### OEIS A144311 Generating function I'm looking for a way to use calculate OEIS A144311 efficiently in Mathematica. First, let's define the series. In one sense or another, this series considers the number between "relative" twin ... 0answers 69 views ### A series in powers of$(a-z)$instead of$(z-a)$Sometimes it is more convenient to find a series expansion (e.g., Taylor, Laurent, Puiseux, ...) in powers of$(a-z)$than in powers of$(z-a)$. For instance, the command ... 2answers 152 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 ... 0answers 95 views ### Peculiarities with Series and fractional exponents or bug? The documentation of the Series[] function states that it can handle "certain expansions involving negative powers, fractional powers, and logarithms." What are the ... 0answers 56 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 ... 2answers 135 views ### Solve of cubic and quartic equations too slow In my problem I have a third order algebraic equation for the variable sigma, all other letters are parameters. Here is it's right-hand side, left hand side is ... 1answer 85 views ### Numerically solving a transcendental equation as a series Given a transcendental equation$f(x,y)=0\$, is there a way for Mathematica to automatically solve the equation as a series? I already know that I can use ...
I need to convert derivatives of g[x,v] wrt v into derivatives wrt x using this relation: $$\frac{dg[x,v]}{dv}=\frac{1}{2}\frac{d^{2}g}{dx^{2}}+\frac{1}{2}\left(\frac{dg}{dx}\right)^{2}$$ This code ...