# Tagged Questions

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

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### Symbolically Expanding One-Variable $q$-hypergeometric Series

In general, how do I get Mathematica to symbolically expand various infinite series to an arbitrary degree of accuracy? I deal with $q$-hypergeometric series quite frequently, and specifically want ...
2k 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 ...
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### Evaluate integral of a series

I want to evaluate this integral, but it won't work. Does anyone knows why? ...
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I have this: ...
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### Asymptotic expansion

I wanted to expand a function of $x$ about $x=\infty$ and see its coefficients as a function of the parameters $m,n,q,y$ and I wrote this - but it didn't work! It gave me back a very complicated ...
195 views

### How to get the series expansion of $e^{x^a}$ at $x=0$?

I want to have a series expansion of $e^{x^a}$ or $e^{c_1x^a+c_2x^b}$ at $x=0$, but Series cannot give any useful result even if the assumption $a>0$ is ...
552 views

### Series coefficients for an infinite sum?

I'm working through Carl Bender's Mathematical Physics lectures on YouTube (which are great fun), and I'd like Mathematica's help solving terms in the perturbation series. It would be convenient if ...
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### Finding series expansion in parametric setting

Suppose $y=f(x;p_1,p_2,...)$ and $t=g(x;p_1,p_2,...)$ are given where $p_1,p_2,...$ are some parameters. We want to find a series expansion of $y$ in terms of $t$. Is there a direct command or ...
616 views

### Series expansion using an exponential basis

I am currently trying to Laplace invert an expression with the following pattern $$\frac{s \alpha \text{Cosh}[s(L-x)]+\beta \text{Sinh}[s(L-x)]}{s(\gamma \text{Cosh}[sL]+s \delta \text{Sinh}[sL])}$$...
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### Problems with series of generalized hypergeometric functions

I have been trying to do the following series: Series[HypergeometricPFQ[{1, 4, 4}, {4 - Sqrt[3], 4 + Sqrt[3]}, z],{z,1,0}] Mathematica says that the result is ...
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### How to get rid of all complex numbers and functions?

For almost esthetical reasons, I always have been fascinated by infinite sums of series and I always wonder if theyhave a closed form. A couple of days ago, I found on MSE a question related to the ...
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### Reducing a multi-variate polynomial to have terms upto certain degree

I have a polynomial in x and y. I want to keep all the terms with (combined) degree 4. Any pointers will be appreciated. Simple tricks for doing the same with univariate polynomial don't seem to work.
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### How to compute the residue of $e^{z-\frac{1}{z}}$ at z=0?

I've tried the following but it didn't work: Residue[Exp[z - 1/z], {z, 0}] not even this: Residue[Exp[1/z], {z, 0}] ...
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### How can we tell Series to treat the expansion parameter as an integer?

It is simple for Mathematica to find an asymptotic expansion for $\frac{1}{-1+p}$ as $p \rightarrow \infty$. However, if we want to restrict $p$ to be an integer and also include some terms that ...
721 views

### How to make all numbers equal to one in a Series?

I have many outputs of one-dimensional Series expansions for which I am only interested in the general tending with the variable. For example, I would like to be able to transform something like <...
284 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 ...
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### equidistant solutions in Sequence Sums That Are Squares

In my demonstration "Sequence Sums That Are Squares" I demonstrate two "lines" of solutions (of infinite length) and ask whether someone can find one more line. I am looking forward to your solution. ...
546 views

### Expansion with binomial coefficients

How can I get binomial coefficients in expansion of $(n x+i) (1+i x)^n+(n x-i) (1-i x)^n$, where $i=\sqrt{-1}$ and $n$ is an integer. I have no idea how to coax Mathematica to do something remotely ...
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### How does Mathematica find a series expansion of expressions containing logarithms when there is a singularity at the expansion point?

I am looking for a good approximation to a function containing logarithms, especially at values close to zero. When I used Mathematica's Series command I found ...
91 views

### Using Product for different variables

when using product in mathematica the initial and maximum value of the product will be the variable itself that will be maupulated. what I need is to make these initial and maximum of the product as ...
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### Solution of equation with power series (perturbation)

So I need to use Mathematica to find the solution of $y=x- \epsilon \sin(2y)$ as a power series in terms of $\epsilon$. I'd assume I'd need to create an equation $f=x-y- \epsilon \sin(2y)$, then ...
2k views

### Switching the axis of a plot [duplicate]

I have a plot but the x and y axis need to be switched. The problem is that I can't explicitly solve for the other so I can change the axis. ...
172 views

### from complex function to a series

How can I express this complex function as a series? Log[ (1 - E^((I Pi (1 - a))/(b - a)) z)/ (1 - E^(-((I Pi (1 - a))/(b - a))) z) ] Where ...