Re: [Boost-users] Stieltjes polynomial

On 22/02/2020 03:25, N A via Boost-users wrote:

Hi

The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and according to Boost article, the Legendre-Stieltjes polynomials (LSp) of degree n=5 and x=0.2 is 0.53239.

So if I want to compute the LSp for n=6, how do I do it? What is the formula you are using to be able to calculate the LSp for any nth degree?

If a recurrence relation is not possible, then is there a closed form mathematical representation to calculate any nth degree LSp?

Please see Patterson, TNL. "The optimum addition of points to quadrature formulae." Mathematics of Computation 22.104 (1968): 847-856 John.

Thanks

On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via Boost-users wrote:

What precisely are you trying to compute? Are you trying to find the coefficients of the polynomials in the standard basis? Are you trying to evaluate them at a point?

Note that the Legendre-Stieltjes polynomials do not satisfy three-term recurrence relations, and so recursive rules (depending on what precisely you mean by that) are not available.

   Nick

‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐ On Wednesday, February 19, 2020 12:07 PM, N A via Boost-users wrote:

...

Hi,

With regard to the article on Boost: Legendre-Stieltjes Polynomials - 1.66.0 https://www.boost.org/doc/libs/1_66_0/libs/math/doc/html/math_toolkit/sf_pol...

Legendre-Stieltjes Polynomials - 1.66.0

Can anyone help me to compute the stieltjes polynomials please? I'm coding in VBA and I'm looking for some recursive rules to calculate same.

Thanks Vick

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