associated legendre functions matlab
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chaitanya acharya
on 7 Dec 2019
Commented: David Goodmanson
on 17 Apr 2020
In the function legendre(1,-0.7071), the value corresponding to P11(-0.7071) is coming wrong when checked with standard solutions. Matlab is giving the solution as -0.7071. whereas, the actual solution is +0.7071. Please have a look at it. Or please suggest me how to correct it.
One can verify using online calculator in the link. https://keisan.casio.com/exec/system/1287453184
6 Comments
Tomy Duby
on 16 Apr 2020
The issue is caused by two different definitions of associated Legendre polynomials:
- with non-negative integers.
- is the definition DLMF (Digital Library of Mathematical Functions) and Matlab are using.
The relation between the two definitions for real x is:
This relation is in the printed edition of Abramowitz and Stegun. I could not find it in DLMF.
I hope this helps.
TD
David Goodmanson
on 17 Apr 2020
Hi Tony,
That's yet another reason why Abramowitz and Stegun is a better book than DLMF. There is a cornocopia of useful equations in A&S, and when they did DLMF you would think they would have supplemented those to make it even better. Instead they threw out a bunch of them and refer you to reference book blah blah blah if you want to find what you need. No excuse for that.
Accepted Answer
David Goodmanson
on 7 Dec 2019
Hi chaitanya,
It's apples and oranges. When the domain of the argument is -1 <= x <= 1, the function is -sqrt(1-x^2). That's what Matlab is doing, and that's what it says it is doing. When the domain is opened up, 0 <= theta < 2pi with x = cos(theta), then the function can become -sin(theta). Both results are in Wikipedia.
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