Opened 6 years ago

# Symbolic orthogonal and some other holonomic polynomials

Reported by: Owned by: rws major sage-wishlist symbolics orthogonal, holonomic N/A

At the moment just the Chebyshev polynomials are symbolic. Missing are `hermite`, `laguerre`, `legendreP`, `legendreQ`, `ultraspherical` (=`gegenbauer`), and, while the Stirling and Euler polynomials are not orthogonal, they are holonomic and belong to the standard repertoire, so we're including them here.

• symbolic Associated Legendre P(n,m,x) / Q(n,m,x) and P(n,x) / Q(n,x) polynomials / functions (#16813)
• symbolic Laguerre / associated Laguerre polynomials (#17151)
• symbolic Gegenbauer polynomials (#20475)
• symbolic Hermite polynomials (#20475)
• symbolic Jacobi P polynomials (#22326)
• symbolic Euler polynomials
• symbolic Stirling polynomials

### comment:1 Changed 6 years ago by vbraun_spam

• Milestone changed from sage-6.3 to sage-6.4

### comment:2 follow-up: ↓ 3 Changed 6 years ago by rws

For the record, using FLINT's `arith_chebyshev_t_polynomial` for `chebyshev_T` in `ZZ[]` is twice as slow as the current Sage implementation.

### comment:3 in reply to: ↑ 2 Changed 6 years ago by fredrik.johansson

Really? For me flint constructs T_10000 in 0.009 seconds while Sage's chebyshev_T takes 1 second.

But *evaluating* a Chebyshev polynomial is a completely different problem. You want to do that by recurrence relations, not by constructing the polynomial and evaluating it.

### comment:4 Changed 6 years ago by rws

Ah, that's true. I only tested at T_500.

### comment:5 Changed 6 years ago by rws

• Branch set to u/rws/make_all_orthogonal_polynomials_symbolic

### comment:6 Changed 6 years ago by rws

• Branch u/rws/make_all_orthogonal_polynomials_symbolic deleted
• Description modified (diff)
• Milestone changed from sage-6.4 to sage-wishlist

The speed issue is now #16812

I think the scope of the ticket is too broad. Let's make it a meta-ticket.

### comment:7 Changed 5 years ago by rws

• Description modified (diff)

### comment:8 Changed 3 years ago by rws

• Description modified (diff)
• Summary changed from make all orthogonal polynomials symbolic to Symbolic orthogonal and some other holonomic polynomials
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