

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 LegendreStieltjes polynomials do not satisfy threeterm 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 Boostusers < [hidden email]> wrote:
Hi,
With regard to the article on Boost:
 LegendreStieltjes 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
_______________________________________________
Boostusers mailing list
[hidden email]
https://lists.boost.org/mailman/listinfo.cgi/boostusers


Hi
The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and according to Boost article, the LegendreStieltjes 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?
Thanks
On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via Boostusers < [hidden email]> 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 LegendreStieltjes polynomials do not satisfy threeterm 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 Boostusers < [hidden email]> wrote:
Hi,
With regard to the article on Boost:
 LegendreStieltjes 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
_______________________________________________
Boostusers mailing list
[hidden email]
https://lists.boost.org/mailman/listinfo.cgi/boostusers


In reply to this post by Boost  Users mailing list
Hi,
For example the Legendre polynomials for degree n=5 and x = 0.2 is 0
On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via Boostusers < [hidden email]> 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 LegendreStieltjes polynomials do not satisfy threeterm 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 Boostusers < [hidden email]> wrote:
Hi,
With regard to the article on Boost:
 LegendreStieltjes 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
_______________________________________________
Boostusers mailing list
[hidden email]
https://lists.boost.org/mailman/listinfo.cgi/boostusers


In reply to this post by Boost  Users mailing list
On 22/02/2020 03:25, N A via Boostusers wrote:
> Hi
>
> The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and
> according to Boost article, the LegendreStieltjes 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): 847856
John.
>
> Thanks
>
>
>
>
> On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via
> Boostusers < [hidden email]> 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 LegendreStieltjes polynomials do not satisfy threeterm
> 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 Boostusers
> < [hidden email]> wrote:
>
>> Hi,
>>
>> With regard to the article on Boost:
>> LegendreStieltjes Polynomials  1.66.0
>> < https://www.boost.org/doc/libs/1_66_0/libs/math/doc/html/math_toolkit/sf_poly/legendre_stieltjes.html>
>>
>>
>>
>>
>>
>> LegendreStieltjes 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
>>
>>
>
> _______________________________________________
> Boostusers mailing list
> [hidden email] <mailto: [hidden email]>
> https://lists.boost.org/mailman/listinfo.cgi/boostusers>
> _______________________________________________
> Boostusers mailing list
> [hidden email]
> https://lists.boost.org/mailman/listinfo.cgi/boostusers_______________________________________________
Boostusers mailing list
[hidden email]
https://lists.boost.org/mailman/listinfo.cgi/boostusers


What is the "triangular system of equations" that need to be solved? And how to solve it?
I'm not familiar with these terms!
However, I came across another article beside yours that dealt with Stieltjes polynomials. Yours deal with Legendre polynomialsStieltjes polynomials, but theirs deal with Legendre function of the second kind with regard to Stieltjes polynomials.
They have a mathematica code, which I don't quite understand but their code yields 1.08169 for the same n and x as below.
Does this mean that we can generate different Stieltjes polynomials with different orthogonal polynomials and/or functions?
Can you help me out please? Thanks
On Saturday, February 22, 2020, 01:26:11 PM GMT+4, John Maddock via Boostusers < [hidden email]> wrote:
On 22/02/2020 03:25, N A via Boostusers wrote: > Hi > > The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and > according to Boost article, the LegendreStieltjes 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): 847856 John.
_______________________________________________
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[hidden email]
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In reply to this post by Boost  Users mailing list
I get the feeling that you want to compute the coefficients of the polynomial in the standard basis:
c0 + c1*x + ...
Unfortunately, this is a bad idea, because the computation is horrifically illconditioned. That's why the boost version expands the LegendreStieltjes polynomials in the Legendre polynomial basisthis is wellconditioned. I vaguely recall that expansion in the Chebyshev basis is also wellconditioned, but we succeeded in the Legendre basis and were happy.
The code, to my eyes, is legible, with references to papers and equations within papers:
What are you trying to accomplish by computing these polynomials? The only application I know of is GaussKronrod quadrature, so I'd be interested if you have another application . . .
‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐
Hi
The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and according to Boost article, the LegendreStieltjes 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?
Thanks
On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via Boostusers < [hidden email]> 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 LegendreStieltjes polynomials do not satisfy threeterm 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 Boostusers < [hidden email]> wrote:
Hi,
With regard to the article on Boost:
 LegendreStieltjes 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
_______________________________________________
Boostusers mailing list
_______________________________________________
Boostusers mailing list
[hidden email]
https://lists.boost.org/mailman/listinfo.cgi/boostusers


In reply to this post by Boost  Users mailing list
> Does this mean that we can generate different Stieltjes polynomials with different orthogonal polynomials and/or functions?
Yes, you can expand every polynomial in every other complete polynomial basis. The basis you select should make the conversion from the original basis wellconditioned.
‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐
On Saturday, February 22, 2020 6:26 AM, N A via Boostusers < [hidden email]> wrote:
What is the "triangular system of equations" that need to be solved? And how to solve it?
I'm not familiar with these terms!
However, I came across another article beside yours that dealt with Stieltjes polynomials. Yours deal with Legendre polynomialsStieltjes polynomials, but theirs deal with Legendre function of the second kind with regard to Stieltjes polynomials.
They have a mathematica code, which I don't quite understand but their code yields 1.08169 for the same n and x as below.
Does this mean that we can generate different Stieltjes polynomials with different orthogonal polynomials and/or functions?
Can you help me out please?
Thanks
On Saturday, February 22, 2020, 01:26:11 PM GMT+4, John Maddock via Boostusers < [hidden email]> wrote:
On 22/02/2020 03:25, N A via Boostusers wrote:
> Hi
>
> The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and
> according to Boost article, the LegendreStieltjes 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): 847856
John.
>
> Thanks
>
>
>
>
> On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via
>
>
> 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 LegendreStieltjes polynomials do not satisfy threeterm
> 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 Boostusers
>
>> Hi,
>>
>> With regard to the article on Boost:
>> LegendreStieltjes Polynomials  1.66.0
>>
>>
>>
>>
>>
>> LegendreStieltjes 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
>>
>>
>
> _______________________________________________
> Boostusers mailing list
>
> _______________________________________________
> Boostusers mailing list
_______________________________________________
Boostusers mailing list
_______________________________________________
Boostusers mailing list
[hidden email]
https://lists.boost.org/mailman/listinfo.cgi/boostusers


In reply to this post by Boost  Users mailing list
Yes, the purpose is to code the GaussKronrod quadrature. Thanks for the link, but I'm not familiar with hpp.
Can you help me out please with the code? I'm ok with Python and VBA!
Or you can tell me the math equation at each step, whichever is more convenient for you.
Thanks
On Saturday, February 22, 2020, 06:07:46 PM GMT+4, Nick Thompson < [hidden email]> wrote:
I get the feeling that you want to compute the coefficients of the polynomial in the standard basis:
c0 + c1*x + ...
Unfortunately, this is a bad idea, because the computation is horrifically illconditioned. That's why the boost version expands the LegendreStieltjes polynomials in the Legendre polynomial basisthis is wellconditioned. I vaguely recall that expansion in the Chebyshev basis is also wellconditioned, but we succeeded in the Legendre basis and were happy.
The code, to my eyes, is legible, with references to papers and equations within papers:
What are you trying to accomplish by computing these polynomials? The only application I know of is GaussKronrod quadrature, so I'd be interested if you have another application . . .
‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐
Hi
The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and according to Boost article, the LegendreStieltjes 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?
Thanks
On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via Boostusers < [hidden email]> 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 LegendreStieltjes polynomials do not satisfy threeterm 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 Boostusers < [hidden email]> wrote:
Hi,
With regard to the article on Boost:
 LegendreStieltjes 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
_______________________________________________
Boostusers mailing list
_______________________________________________
Boostusers mailing list
[hidden email]
https://lists.boost.org/mailman/listinfo.cgi/boostusers


In reply to this post by Boost  Users mailing list
But will both Stieltjes polynomials from the Legendre polynomials and Stieltjes polynomials with Legendre function of the second kind going to work as zeroes for the kronrod weights and nodes?
Because they both yield 0.53239 and 1.08169 for the same n=5 and x = 0.2 !
On Saturday, February 22, 2020, 06:11:33 PM GMT+4, Nick Thompson < [hidden email]> wrote:
> Does this mean that we can generate different Stieltjes polynomials with different orthogonal polynomials and/or functions?
Yes, you can expand every polynomial in every other complete polynomial basis. The basis you select should make the conversion from the original basis wellconditioned.
‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐
On Saturday, February 22, 2020 6:26 AM, N A via Boostusers < [hidden email]> wrote:
What is the "triangular system of equations" that need to be solved? And how to solve it?
I'm not familiar with these terms!
However, I came across another article beside yours that dealt with Stieltjes polynomials. Yours deal with Legendre polynomialsStieltjes polynomials, but theirs deal with Legendre function of the second kind with regard to Stieltjes polynomials.
They have a mathematica code, which I don't quite understand but their code yields 1.08169 for the same n and x as below.
Does this mean that we can generate different Stieltjes polynomials with different orthogonal polynomials and/or functions?
Can you help me out please?
Thanks
On Saturday, February 22, 2020, 01:26:11 PM GMT+4, John Maddock via Boostusers < [hidden email]> wrote:
On 22/02/2020 03:25, N A via Boostusers wrote:
> Hi
>
> The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and
> according to Boost article, the LegendreStieltjes 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): 847856
John.
>
> Thanks
>
>
>
>
> On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via
>
>
> 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 LegendreStieltjes polynomials do not satisfy threeterm
> 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 Boostusers
>
>> Hi,
>>
>> With regard to the article on Boost:
>> LegendreStieltjes Polynomials  1.66.0
>>
>>
>>
>>
>>
>> LegendreStieltjes 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
>>
>>
>
> _______________________________________________
> Boostusers mailing list
>
> _______________________________________________
> Boostusers mailing list
_______________________________________________
Boostusers mailing list
_______________________________________________
Boostusers mailing list
[hidden email]
https://lists.boost.org/mailman/listinfo.cgi/boostusers


In reply to this post by Boost  Users mailing list
I've been able to go through the paper and I have potentially succeeded in calculating the coefficients by means of Gaussian elimination. But I want to make sure, I got it right!
So can you please check for me x=0.2 and n=6,7,8?
Thanks a lot! Vick
On Saturday, February 22, 2020, 06:11:33 PM GMT+4, Nick Thompson < [hidden email]> wrote:
> Does this mean that we can generate different Stieltjes polynomials with different orthogonal polynomials and/or functions?
Yes, you can expand every polynomial in every other complete polynomial basis. The basis you select should make the conversion from the original basis wellconditioned.
‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐
On Saturday, February 22, 2020 6:26 AM, N A via Boostusers < [hidden email]> wrote:
What is the "triangular system of equations" that need to be solved? And how to solve it?
I'm not familiar with these terms!
However, I came across another article beside yours that dealt with Stieltjes polynomials. Yours deal with Legendre polynomialsStieltjes polynomials, but theirs deal with Legendre function of the second kind with regard to Stieltjes polynomials.
They have a mathematica code, which I don't quite understand but their code yields 1.08169 for the same n and x as below.
Does this mean that we can generate different Stieltjes polynomials with different orthogonal polynomials and/or functions?
Can you help me out please?
Thanks
On Saturday, February 22, 2020, 01:26:11 PM GMT+4, John Maddock via Boostusers < [hidden email]> wrote:
On 22/02/2020 03:25, N A via Boostusers wrote:
> Hi
>
> The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and
> according to Boost article, the LegendreStieltjes 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): 847856
John.
>
> Thanks
>
>
>
>
> On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via
>
>
> 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 LegendreStieltjes polynomials do not satisfy threeterm
> 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 Boostusers
>
>> Hi,
>>
>> With regard to the article on Boost:
>> LegendreStieltjes Polynomials  1.66.0
>>
>>
>>
>>
>>
>> LegendreStieltjes 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
>>
>>
>
> _______________________________________________
> Boostusers mailing list
>
> _______________________________________________
> Boostusers mailing list
_______________________________________________
Boostusers mailing list
_______________________________________________
Boostusers mailing list
[hidden email]
https://lists.boost.org/mailman/listinfo.cgi/boostusers


Hi,
I haven't heard from you. I hope all is well?
When you get the time, please check x=0.2 and n=6,7 & 8 for me.
Thanks
On Monday, February 24, 2020, 10:25:20 AM GMT+4, N A < [hidden email]> wrote:
I've been able to go through the paper and I have potentially succeeded in calculating the coefficients by means of Gaussian elimination. But I want to make sure, I got it right!
So can you please check for me x=0.2 and n=6,7,8?
Thanks a lot! Vick
On Saturday, February 22, 2020, 06:11:33 PM GMT+4, Nick Thompson < [hidden email]> wrote:
> Does this mean that we can generate different Stieltjes polynomials with different orthogonal polynomials and/or functions?
Yes, you can expand every polynomial in every other complete polynomial basis. The basis you select should make the conversion from the original basis wellconditioned.
‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐
On Saturday, February 22, 2020 6:26 AM, N A via Boostusers < [hidden email]> wrote:
What is the "triangular system of equations" that need to be solved? And how to solve it?
I'm not familiar with these terms!
However, I came across another article beside yours that dealt with Stieltjes polynomials. Yours deal with Legendre polynomialsStieltjes polynomials, but theirs deal with Legendre function of the second kind with regard to Stieltjes polynomials.
They have a mathematica code, which I don't quite understand but their code yields 1.08169 for the same n and x as below.
Does this mean that we can generate different Stieltjes polynomials with different orthogonal polynomials and/or functions?
Can you help me out please?
Thanks
On Saturday, February 22, 2020, 01:26:11 PM GMT+4, John Maddock via Boostusers < [hidden email]> wrote:
On 22/02/2020 03:25, N A via Boostusers wrote:
> Hi
>
> The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and
> according to Boost article, the LegendreStieltjes 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): 847856
John.
>
> Thanks
>
>
>
>
> On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via
>
>
> 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 LegendreStieltjes polynomials do not satisfy threeterm
> 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 Boostusers
>
>> Hi,
>>
>> With regard to the article on Boost:
>> LegendreStieltjes Polynomials  1.66.0
>>
>>
>>
>>
>>
>> LegendreStieltjes 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
>>
>>
>
> _______________________________________________
> Boostusers mailing list
>
> _______________________________________________
> Boostusers mailing list
_______________________________________________
Boostusers mailing list
_______________________________________________
Boostusers mailing list
[hidden email]
https://lists.boost.org/mailman/listinfo.cgi/boostusers

