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4 votes
0 answers
84 views

Calculate an n-order determinant by FindSequenceFunction

Calculate an n-order determinant: $\left|\begin{array}{cccccc}1 & 2 & 3 & \cdots & n-1 & n \\ n & 1 & 2 & \cdots & n-2 & n-1 \\ n-1 & n & 1 & \cdots ...
lotus2019's user avatar
  • 2,425
3 votes
3 answers
263 views

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 ...
Diego Palomar's user avatar
3 votes
2 answers
264 views

Series solution of a differential equation

Calculate the series solution of a differential equation: $\frac{\mathrm{d} y}{\mathrm{~d} x}=-y-x$, ( $\left.y\right|_{x=0}=2$) AsymptoticDsolvevalue can calculate ...
lotus2019's user avatar
  • 2,425
3 votes
2 answers
258 views

Can Mathematica simplify an ordinary differential equation (ODE) by assuming a power series solution and obtain the recurrence relation?

I have an ordinary differential equation and want to solve it using power series as ψ[x_] = Sum[Subscript[a, n] x^n, {n, 0, ∞}] to obtain the recurrence relation ...
PhysFan's user avatar
  • 63
3 votes
2 answers
312 views

SumConverge does not give a valid result

I wanted to see if the function SumConverge worked for the following summation: $$\sum_{n=1}^{\infty}\frac{\sin^2(n)}{n^p}$$ We can clearly see that for $p>1$ the series converges and for $p\le1$ ...
user372003's user avatar
3 votes
1 answer
119 views

Asymptotic integral expansion at infinity [closed]

Define for all $n\in\mathbb{N}$, a definite double integral, $$I_n= \int_{0}^{1}\int_{0}^{1}\left(\frac{x^2(1-x)y^2(1-y)}{1+x^2 y^2}\right)^n\frac{\cos((2n+1)\tan^{-1}(xy))}{\sqrt{1+x^2y^2}}\ dxdy$$ ...
Max's user avatar
  • 301
3 votes
1 answer
645 views

Multi-dimensional PadeApproximant

I'm trying to approximate a decaying at infinity 2D function f[x_,y_] with a rational function of 2 variables. For a 1D function like that ...
Michael's user avatar
  • 767
3 votes
1 answer
79 views

Order of evaluation of Exp and Normal on result from Series

This may be more math related than Mathematica related, but I thought this might be of interest to the group. I'm trying to work with some Taylor Series approximations of functions that are ...
mikemtnbikes's user avatar
3 votes
1 answer
75 views

Approximating exponential generating function (EGF) from values of generating function (OGF)

I have a function that can evaluate ordinary generating function, and need to construct an approximation to the exponential generating function by using a few calls to the ordinary generating function....
Yaroslav Bulatov's user avatar
3 votes
1 answer
88 views

Expanding in small but non zero quantity

I am trying to deal with a function which diverges at $r=0$. I encountered the following function $$f(r)=\int_0^1\frac{x^2(2-x)}{1-x+rx^2}\mathrm dx$$ The paper says that in the limit $r\ll1$, it ...
Markon's user avatar
  • 133
3 votes
1 answer
177 views

Generating function for residues of a complicated function

I have a rather complicated function involving 3F2 Hypergeometric functions (see below), which has infinitely many poles. I can extract the residues individually. But it would be great if I could ...
Physics Moron's user avatar
3 votes
0 answers
85 views

Asymptotic expansion for a function containing irrational exponents

I'm trying to find an asymptotic expansion of a function containing irrational exponents in the form of a power series (which also might contain irrational exponents). It works correctly if I request ...
Vladimir Reshetnikov's user avatar
3 votes
0 answers
140 views

Cannot Understand nth Derivative of x/ArcTan[x]

The nth derivative of x/ArcTan[x]: f[x_, n_] = D[x/ArcTan[x], {x, n}] Evaluates to: I cannot get this general from to return ...
Josey Stevens's user avatar
3 votes
0 answers
231 views

Negative result of a integral of positive function

Let's try this: I have a function of two arguments, $e$ and $\omega$. First I integrate some function of $(e, \omega)$: ...
user16320's user avatar
  • 2,396
3 votes
0 answers
142 views

Error when simplifying a series expression

I have the following function which I call FF[q_,y_,u_] and this function is well known to have a reasonable Taylor expansion in all three variables. For example, ...
Benighted's user avatar
  • 1,337
2 votes
2 answers
331 views

Asymptotic integral computation takes too long

I am trying to understand how grows the function $k\mapsto\int_{0}^{\infty} \left({1 - \left(1 - \exp(-t/k)\right)^k}\right)dt$ for $k\to\infty$, and I expect a result asymptotically equal to $k\log(k)...
Penelope Benenati's user avatar
2 votes
3 answers
181 views

FindSequenceFunction on trigonometric series

I want to get the sine series general expression of the following two functions by FindSequenceFunction. (1) $f(x)=\left\{\begin{array}{l}0,-2 \leqslant x<0, \\ ...
lotus2019's user avatar
  • 2,425
2 votes
2 answers
369 views

Series for Sin[x] with specific notation

I'm trying to get mathematicas series function for Sin[x] to output a result that look like this: $\sin x=\sum_{n=0}^{\infty} \frac{(-1)^{n}}{(2 n+1) !} x^{2 n+1}$ ...
lotus2019's user avatar
  • 2,425
2 votes
3 answers
167 views

Find Generalized Series with Symbolic Variable

CoefficientList[Series[Exp[x], {x, a, 3}], x] Gives the following expression, $$ \left\{-\frac{1}{6} e^a a^3+\frac{e^a a^2}{2}-e^a a+e^a,\frac{e^a a^2}{2}-e^a a+e^...
Torkoal's user avatar
  • 153
2 votes
3 answers
320 views

How to get out coefficient of term in series?

Suppose I have a function $f(s,t) = [(1-t^2)(1-s^2t^2)]^{-1/2}$. Is there a way to get the general coefficient in this power series of the form $s^{2k} t^{2n}$?
Gregory's user avatar
  • 381
2 votes
2 answers
302 views

Series expansion using binomial theorem in Mathematica

The series expansion of $\displaystyle\left(1-\frac{a}{x}\right)^{1/3}$ using the Binomial theorem is given by $$\displaystyle\left(1-\frac{a}{x}\right)^{1/3}=1-\frac{a}{3x}-\frac{a^{2}}{9x^{2}}-\...
VH84's user avatar
  • 179
2 votes
2 answers
218 views

Finding number of terms determined by the error for sum of series

So inf is the actual numerical value taken of the sum from $n=0$ to $n=\infty$ for $(-1)^n/(3n+1)$. Now I'm trying to find how many terms I need so that the sum of ...
Laura's user avatar
  • 73
2 votes
2 answers
149 views

Series for $(1+x)^{m}$ with specific notation

I'm trying to get mathematicas series function for $(1+x)^{m}$ to output a result that look like this: $(1+x)^{m} = \sum_{n=0}^{\infty} \frac{m !}{n !(m-n) !}x^{n}$ However, ...
lotus2019's user avatar
  • 2,425
2 votes
1 answer
186 views

Mathematica just takes infinite time to solve this

Can You help? I don't even care about the exact solution. I will be satisfied by the series expansion of the result around a=0. I tried to solve by series expansion and the same result .. infinite ...
Ahmed Kamal Kassem's user avatar
2 votes
2 answers
884 views

Series expansion of integral

I'm looking for a way to do a series expansion of $$\frac{\mu_0bI_0}{4\pi}\int_0^{2\pi}\frac{\cos\left[\omega\left(t-\frac{1}{c}\sqrt{r^2+b^2-2rb\sin(\theta)\cos(\phi)}\right)\right]}{\sqrt{r^2+b^2-...
Bo Johnson's user avatar
2 votes
2 answers
402 views

Asymptotic solution of the saddle-point equation

As an example we have the following equation: $$\sum _{j=1}^{\infty } \frac{r^j}{\left(1-r^j\right)^2}=n$$ Sum[r^j/(1 - r^j)^2, {j, 1, Infinity}] == n I'm ...
Vaclav Kotesovec's user avatar
2 votes
2 answers
148 views

Strange failure of Series and Derivative

I just spend three hours and posted two Questions trying to figure something out, and it turned out all the confusion was caused by this mysterious quirk. I want to expand g[x,v] in v at v=0, using ...
Jerry Guern's user avatar
  • 4,642
2 votes
4 answers
364 views

Series expression of a RootSum object

Mathematica was not able to calculate the definite integral of a trigonometric function of mine: ...
JI-br's user avatar
  • 23
2 votes
1 answer
83 views

Why does Series give two different results for given function?

I want to do Series of this function x^12 Cos[y x]^2 Sin[y x]^6 Sin[(-1 + Sqrt[3]) y x]^2 around ...
Martha97's user avatar
  • 349
2 votes
2 answers
257 views

Multivariate series for approximating implicit system

I'm trying to approximate the solution of an implicit set of equations by means of a Taylor series. I have managed to do so for a solution expressed in terms of a single independent variable, by using ...
Marijnn's user avatar
  • 297
2 votes
1 answer
208 views

Problem with SeriesData

Problem: I need to find the leading order term in an expansion whose leading order behavior is a priori unknown. I can of course go with Series and try different orders, say ...
SonerAlbayrak's user avatar
2 votes
3 answers
349 views

Mathematica failing to series expand a simple analytic function

Bug introduced in 5.0 or earlier and persisting in 11.2 Mathematica is doing funky things with the function ...
tparker's user avatar
  • 1,866
2 votes
1 answer
2k views

Asymptotic forms of Bessel function [closed]

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 ...
Hedin's user avatar
  • 103
2 votes
1 answer
94 views

Mathematica integrates centered functions, but can not integrate shifted ones

Mathematica seems to integrate this function: $\int \limits_{-\infty}^{\infty} d w\, \frac{\sin ^2\left(\frac{1}{2} wt \right)}{w^2} \frac{\frac{\gamma ^2}{4}}{ \left(w^2+\frac{\gamma ^2}{4}\right)}$, ...
andrix's user avatar
  • 153
2 votes
1 answer
173 views

Working with Limit on a Root expression

I am trying to diagonalize a somewhat larger matrix that is dependent on several parameters. Applying, say, Eigenvalues to that matrix is quite straightforward, but ...
ranguwud's user avatar
  • 143
2 votes
1 answer
263 views

Unable to evaluate the Limit of an expression at Infinity, with assumptions on parameters

I need some help in evaluating the following limit with assumptions: ...
user avatar
2 votes
1 answer
167 views

Series applied to an infinite sum does not work

When I have Sum[(-1)^n x^(n^2) y^n, {n, 0, ∞}] and I try evaluating ...
Camilo's user avatar
  • 85
2 votes
1 answer
344 views

Evaluate an Exponential involving an Integral Operator

How would I tell Mathematica to evaluate something like \begin{align*} \exp\left[\int_a^b dx\right]f(x)\equiv f(x)+\int_a^b f(x)dx+\frac{1}{2!}\int_a^b\int_0^{x}f(x')dx'dx+\frac{1}{3!}\int_a^b\int_0^{...
user85503's user avatar
  • 1,002
2 votes
2 answers
1k views

About generating power series

For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows, ...
user6818's user avatar
  • 1,191
2 votes
1 answer
799 views

About high dimensional integrals

I want to be able to do high dimensional integrals like, (..naively I wrote it as this..) ...
user6818's user avatar
  • 1,191
2 votes
0 answers
197 views

Symbolic perturbation expansion for quantum mechanics using Hellmann-Feynman derivaties

I am interested in some quantum mechanical perturbation expansion for energies. Actually I want to implement these terms $E_n^{(k)}$. As is stated below one can do that using CAS. I would be ...
Raphael J.F. Berger's user avatar
2 votes
0 answers
186 views

Formal Power Series and 0^0

I'm having the following problem: I define series = Exp[Sum[Subscript[J, n]/n t^n, {n, 1, \[Infinity]}]] and it's all fine. Also when I ask Mathematica ...
MaPo's user avatar
  • 909
1 vote
2 answers
134 views

Series expansion for two limits of x [closed]

I have a function f($x$) given by the expression $$f (x) = \frac{\left(1+x\left[1-\sqrt{1+x^2}\right]\right)^2-x+x^3\left[1-\sqrt{1+x^2}\right]^2}{1+x^2\left(1-\sqrt{1+x^2}\right)^2}$$ and would like ...
miniplanck's user avatar
1 vote
1 answer
247 views

Maclaurin Series - Table

I'm starting to learn Mathematica. I have to solved this eq and draw the graph. It is developing a series of Taylor in about x0 == 0. This is my equation to solve <...
Karol's user avatar
  • 29
1 vote
2 answers
139 views

Finding an elementary function growing asymptotically as the integral of a sequential product

I am trying to understand how grows the function $f:\mathbb{N}\to\mathbb{R}$ Integrate[(1-Product[1-Exp[-2*j*t/(k*(k+1))], {j, 1, k}]), {t,0,\[Infinity]}] for $k\to\...
Penelope Benenati's user avatar
1 vote
1 answer
537 views

Laurent series 0 < |z-3| < 3

I wanna check my laurent series exercises on Mathematica, but can't seem to find a command or program to achieve the result of such type of interval. $f(z)=\frac{1}{(z-3) z},\\1<|z-3|<3$ The ...
Vinholi's user avatar
  • 13
1 vote
3 answers
229 views

How to express the function $a(t)$ knowing a parametrization $a(\eta)$ and $t(\eta)$?

I have this function : \begin{equation}\tag{1} a(\eta) = \sqrt{\sin{2 \eta}}, \end{equation} and this time variable : \begin{equation}\tag{2} t(\eta) = \int_0^\eta a(\eta') \, d\eta'. \end{...
Cham's user avatar
  • 4,133
1 vote
1 answer
242 views

Discrepancy with Hurwitz Zeta function

I've come across an issue while using Wolfram Mathematica that I don't quite understand. Consider the following symbolic computation: ...
stefan_chem's user avatar
1 vote
1 answer
135 views

Asymmetric multivariable Taylor expansion

I want to expand a two-variable function up to asymmetric orders in two expansion variables, i.e. $$f(x,y) = T[f(x,y)] + \mathcal{O}(x^2,y^3,xy,xy^2).$$ Note that, while quadratic terms in $y$ are ...
Pablo G's user avatar
  • 13
1 vote
1 answer
151 views

Taylor's theorem approximation [closed]

I'm struggling to determine an estimate for a function (e^-x) using the taylor theorem and getting a truncation error as well. I've tried using the series function but that doesn't let me apply a=0.
Renae's user avatar
  • 13