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

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1answer
49 views

Plot CPU time vs iteration? [duplicate]

I would like to generate a plot of CPU time vs number of iterations. For example, if I were to calculate the solution of a system of differential equations in state-space form using the summation of ...
0
votes
1answer
88 views

How to calculate the unknown quantity in an infinite series?

I'd like to calculate x value in this equation. Basically, I tried to 2 types of method which are FindRoot and NSolve. But, I have failed the calculation caused by these errors up to now. If ...
0
votes
1answer
72 views

Problem of how to manipulate Taylor/McLaurin series

I'm new to Mathematica so I don't know very well the program itself. I would like to manipulate as he does this person in youtube: http://www.youtube.com/watch?v=fCJHvQaGNiQ But I put all the ...
1
vote
1answer
38 views

Power series with decimal and arbitrary powers

Is there a way to make Mathematica do a series of the form: Series[ E^{\beta}$ , {x, 0, 1}] I have noticed that ...
-1
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0answers
18 views

Finding out the wrong number in the series [migrated]

I need to find the wrong number in the following series.Device a logic to find the wrong number. 2,2,6,52.5,157.5,630 And 2,12,28,72.2,152,312,632 Regards
0
votes
0answers
26 views

Speed up series expansion [duplicate]

I have a rather complicated function that I need to expand it in series, which is quite straightforward but takes a long time. I was wondering if there is a way to speed up such a calculation: ...
0
votes
3answers
80 views

How to use Assumptions in a Series Expansion

I want to series expansion the expression $\frac{1}{2} \left(e_1+e_2-\sqrt{e_1^2-2e_1e_2+e_2^2+4V_{12}^2} \right)$ up to second order in $V_{12}$ using the assumption $e_1>e_2$. So I tried ...
3
votes
4answers
117 views

Exponential of a Differential Operator

In Mathematica, is it possible to exponentiate a differential operator such that the operator will act on a function, $f(x,p)$? Specifically, I wondering if I can get Mathematica to do this: ...
0
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0answers
47 views

How to power-series expand determinants?

Say $g$ is a matrix which is given as, $g = g_0 + xg_2 + x^2 g_4 .. +x^{d/2 -1}g_{d-2}+ x^{d/2}(g_d + h_d(log (x)))$ where $d$ is an even number and each $g_i$ is a matrix (same dimension as $g$) and ...
0
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1answer
62 views

How do I plot a Taylor polynomial of various degrees in two variables?

I want to plot the Taylor polynomials of $f(x,y)= Sin(1 + x + y^2)/(4 + x^2 + y^2)$ of degrees 4 and 7 around the point $(0,0)$ over the rectangle $[-\pi,\pi]\times [-\pi,\pi]$ I am currently using ...
0
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3answers
84 views

Create polynomials from Series

This question actually doesn't have quite a lot to do with the Series function, but I don't know how to describe my problem. So here's the thing. I'm trying to ...
5
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0answers
148 views

Why is this infinite series wrongly computed by Mathematica?

Could you let me know if Mathematica (newer versions) is able to correctly compute this one? Sum[(-1)^(n + 1) Cos[3^n x]^3/3^n, {n, 1, Infinity}]
1
vote
1answer
70 views

divergent part of a series

I am trying to find a function that gives me the divergent part of series in any case. The method "Series[]" does not work because Series[42,{n,0,-1}] gives as ...
1
vote
1answer
48 views

Series and that old ivar error

I am trying to compare plots of the function (1+x)^{1/3} and its power series. The code for the power series generates an error message referring to an invalid variable: 'General::ivar: -1.09993 is ...
2
votes
1answer
98 views

Remove singularity at zero from $-((i^{-n} (-1 + i^n)^2)/(n^2 π^2))$

The expression h[n_] = -((I^-n (-1 + I^n)^2)/(n^2 π^2)) is real for all integers n. Although indeterminate at ...
0
votes
1answer
45 views

Plot Series output? [closed]

I tried to search if similar questions existed but I have not found anything. Can someone help me with this code? ...
0
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1answer
59 views

Working with means and variances

My goal is to work out on the following equation: $$Mean(P)(1-Mean (P))\left (h + (1 - 2 h) (1 - \frac {Var (P)} {Mean (P) (1 - Mean (P))}) (1 - Mean (P)) + \frac {Var (P)} {Mean (P) (1 - Mean ...
2
votes
1answer
69 views

Taylor expansion of function of vectors—simplifying the output

I've got a real-valued function of several vectors $f(u,v,w)$ formed by taking scalar products of linear combinations of the vectors, I want to Taylor expand around small $v$ by writing $$f(u,\delta ...
1
vote
1answer
47 views

Compose two special power series expansions

I have two functions $A(x), B(x)$, given in a special power series form: $A(x)=1-x^{2}\left(\frac{a}{10}-\sum_{k=1}^{9}b_{k}\left(\frac{(x^{2}-1)}{r}\right)^{k}\right)$ ...
2
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2answers
90 views

Bessel derivatives

I tried to expand BesselJ[k,x] function into a Taylor series with Series command. Here both ...
0
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0answers
72 views

A power series expansion

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 $n \in \mathbb{Z}$ and ...
0
votes
1answer
91 views

About doing an sum

I want to explain this summation to Mathematica, For $a >0$ define $n_u, n_d \in \mathbb{Z}$ such that if $\{ a \} \leq 0.5$ then $n_u = [a]-1$ and $n_d = - [a]$ and if $\{ a \} > 0.5$ then ...
6
votes
1answer
109 views

Is it possible to circumvent a bug inside SeriesCoefficient?

As far as I can tell, there seems to be a bug in SeriesCoefficient: ...
2
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1answer
100 views

Matrix exponential MatrixExp[] vs Sum[MatrixPower[]] doesn't match?

I might be an idiot, but I cannot get the manual expansion of e^At to match the MatrixExp[A t] result. For example, I have the following: ...
1
vote
1answer
75 views

How to expand function $\cos(y+i\log{x})$ in powers of $x$?

I have the following, probably very simple question. How can I get $\it{Mathematica}$ to power expand function $\cos(y+i \log(x))$ in powers of $x$? This function obeys a well defined Laurent ...
0
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1answer
111 views

How to simplify power series in terms of functions

For example, after some computations mathematica outputs $$ \sum_{k=0}^{\infty} \frac{k g_k z^{k+4}}{(1-z)^3} $$ and we assume that $$G(z)= \sum_{k=0}^{\infty} g_k z^k $$ so the question is: how ...
0
votes
1answer
85 views

How could I expand this equation

How could I expand this equation (0.837 + x^0.5 + x)^4.870 Neither Expand[(0.837 + x^0.5 + x)^4.870] nor ...
0
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1answer
56 views

nested series expansion

I have to invert the following matrix in which the functions U[t,x,y,r] and K[t,x,y,r] and all their derivatives are "small"; ...
0
votes
1answer
87 views

Multivariate series expansions to different powers

I have a function that (I believe) correctly takes the multivariate Taylor series expansion about the origin for some expression (first argument), in some variables (second argument, list), to ...
0
votes
2answers
45 views

Expand expression into quotient of negative power series

I have a function T(z) and want to expand it to the following form: At the end I want to have a list of equations, which can calculate a0, a1, a2, b0, b1 and b2 with different values of h1, h2, ...
1
vote
2answers
141 views

Making mathematica do regulated integrals

Consider the integration, $\int _0 ^\infty dx\ x \tanh( \pi x) \sqrt {x^2 + a^2 } $ where $a$ is a real number. This integral is divergent. We note that an asymptotic expansion of the integrand ...
1
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0answers
80 views

Imaginary number appears in Integrate [closed]

I had a problem in the following code because when I use Integrate, there will always be imaginary number in the result. I put my code here. The satisfactory result should look like eq 9.138, which I ...
2
votes
1answer
97 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 to ...
9
votes
1answer
500 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 ...
0
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1answer
93 views

Evaluate integral of a series

I want to evaluate this integral, but it won't work. Does anyone knows why? ...
4
votes
1answer
181 views

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 ...
5
votes
2answers
149 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 ...
3
votes
3answers
155 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 ...
1
vote
2answers
55 views

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 ...
1
vote
1answer
111 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])} ...
3
votes
1answer
132 views

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 ...
3
votes
1answer
231 views

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 ...
1
vote
1answer
64 views

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. ...
5
votes
1answer
155 views

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}] ...
1
vote
1answer
60 views

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 ...
6
votes
3answers
310 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 ...
0
votes
2answers
127 views

Asymptotic series

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 ...
-1
votes
1answer
65 views

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. ...
1
vote
2answers
146 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 ...