# Tagged Questions

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

54 views

### Asymptotic solution

I have an ODE V''[z] + ( (I z0^2 w)/(3 (z - z0)^2) + (2 - (4 I z0 w)/9)/(z - z0)) V'[z] + (-(12/41) I z0 w + (23 z0^2 w^2)/369)/(z - z0)^2 V[z] == 0 ...
85 views

256 views

### 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 ...
81 views

### Weird SeriesData behavior?

I was trying to calculate the determinant of a matrix whose elements are truncated series. As a result I obtained an expression like this: ...
141 views

### FindSequenceFunction for sum of hypergeometric terms?

The built-in function FindSequenceFunction is quite good at recognizing hypergeometric terms, i.e. terms $c_k$ for which $c_{k+1}/c_k$ is a rational function of $k$....
112 views

### Series expansion of $(x;x)_\infty$ at $x=1^-$?

The so called Euler function is implemented in Mathematica as QPochhammer[x, x] I have been trying to obtain its leading behavior for $x\to 1$ from below. ...
64 views

### Automation of Perturbation Solution

I'm trying to solve an equation of the form $$R(\theta)f(\theta)+hg(\theta) = 0$$ for small $h$, where $R$, $f$, and $g$ are functions. I've assumed a power series expansion for $\theta$ in terms ...
165 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 ...
922 views

### Partial fraction decomposition of $1/(e^x-1)$

This link has discussion on finding partial fraction decomposition of $1/(e^x-1)$, so I experimented with Mathematica to see if M can do it, but looks like not. Similar is the case with one more CAS I ...
42 views

### Behavior of solution to a ODE near a singular point [closed]

I want to see how the solution to the following ODE looks near z=z0. ...
1k views

### Calculating Taylor polynomial of an implicit function given by an equation

I'd like to write a procedure that will take an equation: F(x,y,z) = 0 chosen variable: x a point: ...
175 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 ...
208 views

### Is there a function that, given a rational function, will return the general term of its infinite series expansion?

Is here some way to expand a rational function to an infinite sum in Mathematica, i.e., a series? I want the general term of the series. For example, $\dfrac{2}{3(x-1)^3}$
259 views

### Asymptotic forms of Bessel function

I want to replace Bessel functions by asymptotic forms, so the question is: can I find the best ones with help of Mathematica? And if it's possible, how can I do it? Update How can I get with ...
43 views

### Series expansion in Infinity issue with Zeta(s) function

With this code: Series[Zeta[s], {s, Infinity, #}] & /@ Range[10] // MatrixForm Series expansion for the Zeta(s) ...
472 views

### Chebyshev Approximation

Is there functionality in Mathematica to expand a function into a series with Chebyshev polynomials? The Series function only approximates with Taylor series.
38 views

### Maclaurin Series Help [closed]

My problem is to numerically approximate the series (1 - Cos[x])/x over the interval [0,1]. I typed it into Mathematica as so: ...
55 views

### Can highlight an expression in mathematica in an expansion?

I ask mathematica to make an expansion of some expression. Is there a way to ask mathematica to highlight all terms that, say, goes by x^3 since it is really hard to find them? E.g. ...
242 views

### A power series expansion [closed]

Consider the function, $f(z) = z\, \tanh(\pi z) \log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ ...
77 views

### Ramanujan's asymptotic formula for $p(n)$ [closed]

The following expression is the exact formula of partition function. Ramanujan's asymptotic formula for $p(n)$ is following $$p(n)\sim\frac{1}{4n \sqrt{3}}e^{\pi \sqrt{2n/3}}$$ Can I use ...
86 views

### Bug in Series[Pochhammer[1+n, n], {n,Infinity,1}]?

The function Pochhammer[1 + n, n] tends to infinity. We have ...
79 views

### Find the function $f(x)$ by using its fourier expansion

It is easy to find the fourier coefficient and fourier expansion of $f(x)$ function. But I want solve the inverse problem by using Mathematica How to find the function $f(x)$, if I know its ...
44 views

### Unexpected imaginary term in the asymptotic expansion of DawsonF

FullSimplify[Series[2 DawsonF[x], {x, âˆž, 8}]] (* -I Exp[-x^2] âˆšÏ€ + (1/x + 1/(2 x^3) + 3/(4 x^5) + 15/(8 x^7) + O[1/x]^9) *) What is the reason the term ...
30 views

72 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 ...
56 views

### break down the function

I am using Series function, but I found that it cost too much time. Since the Series function is Taylor expansion and I only need first order, I want to break down the code, so I can make it faster <...
100 views

### Is there a compact way to Taylor expand all the terms in the equation?

For example a vector: ...
60 views

### Sum of Infinite convergent series

I have a series as Sum[(x^1 - (x - 1)^1) (b^Log[(1 + (x))]), {x, 1, Infinity}] which is convergent when b=0.3 and ...
How can I use Mathematica to expand such a product (only need a finite number of terms): $$\prod^{\infty}_{n=1}\frac{({1-yq^{n+1}})({1-y^{-1}q^n})}{(1-q^n)^2}$$