9711

The Deltafunction as the Limit of Some Special Functions

Another Demonstration gives some representations for the Dirac deltafunction as the limit of elementary functions (see the related links below).This Demonstration illustrates several additional limiting relations involving special functions and the deltafunction:
Bessel: , (
Airy: .
Hermite: The derivative of the deltafunction is given by . Shown is with .
Dirichlet kernel: , where the delta-comb or shah function is defined by . This is a periodic extension of the deltafunction.
Fejér kernel: , with the same periodicity as the Dirichlet kernel.
Sigmoid: The derivative of the sigmoid function: .
Closure: An orthonormal set of functions {} obeys the closure relation . This is shown for orthonormalized Hermite functions with .

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Snapshot 1: Bessel function representation with All but the leftmost peak will produce canceling contributions as
Snapshot 2: approach to using Hermite polynomial
Snapshot 3: closure relation approaching
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+