Back Transformation for Legendre Polynomials

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Discussion Overview

The discussion revolves around Legendre polynomials, focusing on their properties, applications, and a specific inquiry regarding back transformation for plotting estimated coefficients from a fitted polynomial.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant seeks a general explanation of Legendre polynomials.
  • Another participant requests clarification on what the inquirer already knows to provide a more targeted response.
  • A third participant provides a link to a resource and describes Legendre polynomials as dependent on a continuous variable and integers, noting their orthogonality and usefulness in spherical coordinates and potentials.
  • A later post from a participant named Roberto asks for assistance with back transformation to plot classes using coefficients from a fitted 7th order Legendre polynomial.

Areas of Agreement / Disagreement

There is no consensus on the specifics of Legendre polynomials, as participants express varying levels of knowledge and focus on different aspects of the topic.

Contextual Notes

Some assumptions about prior knowledge and specific applications of Legendre polynomials remain unaddressed, and the inquiry about back transformation lacks detailed context regarding the fitting process.

WARGREYMONKKTL
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some body who can explain for me the Legndre polynomials:eek: :eek:
 
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What do you want to know and what do you already know about them:eek: :eek:

Surely, nobody will be willing to type the whole theory behind them so be more specific please:eek: :eek:
 
http://mathworld.wolfram.com/LegendrePolynomial.html

A set of polynomials dependent on continuous variable x and integers m (and sometimes n) which have useful orthogonality and spanning properties.

Known to have useful solutions when dealing with spherical coordinates and potentials. Want more info? There's a fantastic website I know called Google. It'll find anything for you ;)
 
Legendre Polynomials

I need some help. I fitted a 7th order legendre polynomial and got the L0 to L7 coefficients for different classes. How can I get a back transformation in order to plot each class using the estimated coefficients?
Thanks to anybody.
Roberto.
 

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