Linked Questions

0 votes
2 answers
174 views

The coefficients with NIntegrate [duplicate]

I try to compute the coefficients b[i] , $i=2,...,m$. I got the following output: ...
Khaled's user avatar
  • 71
50 votes
9 answers
13k views

About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...
yulinlinyu's user avatar
  • 4,825
34 votes
5 answers
15k views

How can I differentiate numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
lachis83's user avatar
  • 1,749
26 votes
3 answers
14k views

How to solve ODE with boundary at infinity

y''[x] - x y[x] == 0 y[0] == AiryAi[0], y[∞] == 0 The analytic solution to this ODE is the Airy function y[x] == AiryAi[x] if ...
3c.'s user avatar
  • 669
38 votes
2 answers
6k views

Determining which rule NIntegrate selects automatically

I need to numerically integrate a highly oscillatory function over the semi-infinite domain $(0,\infty)$: $$\int_0^\infty \frac{\sin^2(x) \sin^2(1000 x)}{x^{5/2}}\mathrm dx$$ Since the Levin rule (...
user7885's user avatar
  • 381
60 votes
1 answer
3k views

What's inside InterpolatingFunction[{{1., 4.}}, <>]?

I'm curious what's inside the InterpolationFunction object? For example: ...
xslittlegrass's user avatar
9 votes
6 answers
8k views

Series expansion in terms of Hermite polynomials

I am trying to expand a polynomial in terms of orthogonal polynomials (in my case, Hermite). Maple has a nice built-in function for this, ChangeBasis. Is there a ...
prazuber's user avatar
  • 429
21 votes
4 answers
3k views

Interpolating data with a step

Suppose I have some data with a step in it: data = {{1, 1}, {2, 2}, {3, 3}, {3, 4}, {4, 5}, {5, 6}}; Interpolation will complain about this and not give you an ...
wxffles's user avatar
  • 14.2k
8 votes
5 answers
2k views

Convert polynomial to Chebyshev

I want to convert a polynomial in "standard form" to Chebyshev form. Here's one way to do it: ...
user avatar
8 votes
4 answers
1k views

How can I find the inverse of an interpolating function?

I am numerically solving the coupled differential equations (for $t[\tau]$ and $r[\tau]$) below. Mathematica outputs two interpolating functions as solutions. I would like to invert one of these ...
Aiden's user avatar
  • 181
9 votes
2 answers
857 views

Analytical approximation of indefinite integral on a given interval to a given precision

I'm looking for an analytical approximation of $\int_a^b e^{-x^2}\mathrm{erf}(x+c) dx$ that would be accurate to precision $\varepsilon$ for $a,b,c$ within a certain range. How do I ask Mathematica ...
Michael's user avatar
  • 767
4 votes
3 answers
475 views

FunctionInterpolation over an open interval

I'm trying to obtain an arc-length parametrization of a spline curve as per https://mathematica.stackexchange.com/a/8456. To do so, I need to calculate partial derivatives of such curve and then ...
Marco's user avatar
  • 317
6 votes
1 answer
597 views

Precompiling a Whittaker function

Is there a way to speed up the evaluation of special functions in Mathematica? I am particularly interested in the Whittaker W function. For instance, the following piece of code: ...
Alex's user avatar
  • 775
2 votes
3 answers
909 views

Find all roots of a function with parabolic cylinder functions in a range of the variable

I want to find all roots of a function involving Parabolic Cylinder Functions. In what follows, I define 2 variables $\xi1$ and $\xi2$, which in turn depend on $\omega$. My function is then defined as ...
Ambrose Chau's user avatar
3 votes
3 answers
584 views

Finding a polynomial representation for a sum function

I'm trying to find a polynomial representation for this horrendous function: $$f(x)=\frac{\frac{1}{2}-\frac{4}{1+10,000x}\sum_{n=0}^{\infty}\frac{(-1)^n}{\big[\big(n+\frac{1}{2}\big)\pi\big]^4}\tanh\...
VortexSheet's user avatar

15 30 50 per page