Find Legendre Polynomials of Order 15+

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Discussion Overview

The discussion revolves around finding Legendre Polynomials of order 15 and above. Participants explore various methods for obtaining these polynomials, including recursion formulas and software tools.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant requests a list of Legendre Polynomials of order 15 and above, indicating difficulty in finding such resources online.
  • Another suggests using recursion formulas to derive the polynomials, noting that high-order polynomials are not commonly listed.
  • A different participant mentions that Mathematica can be used to obtain these polynomials and offers to assist further if more specific information is provided.
  • One participant recommends searching online for references, providing links to resources that may contain relevant information.
  • A participant questions whether Rodrigues' formula can be used to derive the coefficients of the terms in the polynomials.
  • Another participant shares the explicit form of the 14th order Legendre Polynomial, showcasing a specific example of the polynomial's coefficients.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the availability of Legendre Polynomials of order 15 and above, with multiple suggestions and methods proposed without agreement on a single solution.

Contextual Notes

Some methods mentioned depend on access to specific software or online resources, and there may be limitations in the availability of high-order polynomials in standard references.

Who May Find This Useful

This discussion may be useful for students or researchers looking for methods to obtain high-order Legendre Polynomials, particularly those interested in mathematical physics or applied mathematics.

thepaqster
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Hey there, does anyone know where I could find a list of Legendre Polynomials? I need them of the order 15 and above, and I haven't been able to find them on the net.
Thanks!
 
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Well you could use the recursion formulae. I haven't seen them listed too high anywhere.
 
You can get them out of Mathematica, or something like that. If you don't have access to it, tell me exactly what you want to know.
 
Does not the Rodrigues' formula eventually give you coefficients of the terms ?
 
Here's the 14th order:
[tex]-\left( \frac{429}{2048}<br /> \right) + <br /> \frac{45045\,x^2}{2048} - <br /> \frac{765765\,x^4}{2048} + <br /> \frac{4849845\,x^6}{2048} - <br /> \frac{14549535\,x^8}<br /> {2048} + <br /> \frac{22309287\,x^{10}}<br /> {2048} - <br /> \frac{16900975\,x^{12}}<br /> {2048} + <br /> \frac{5014575\,x^{14}}{2048}[/tex]
Aren't I nice?
 

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