Orthogonal Polynomials

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Orthogonal Polynomials

A brief proposal for providing a complete suite of orthogonal polynomials as PyTorch operators. Enjoy!

One of a five-part series of special functions issues:

• Gamma and Related Functions (Gamma and Related Functions #78065)
• Bessel and Related Functions (Bessel and Related Functions #76324)
• Orthogonal Polynomials (Orthogonal Polynomials #80152)
• Elliptic Functions and Integrals (Elliptic Functions and Integrals #80157)

API

Chebyshev Polynomials

• chebyshev_polynomial_t(input: Tensor, n, *, out=None) → Tensor

Chebyshev polynomial of the first kind $T_{n}\left(\text{input}\right)$.

• chebyshev_polynomial_u(input: Tensor, n, *, out=None) → Tensor

Chebyshev polynomial of the first kind $U_{n}\left(\text{input}\right)$.

• chebyshev_polynomial_v(input: Tensor, n, *, out=None) → Tensor

Chebyshev polynomial of the first kind $V_{n}\left(\text{input}\right)$.

• chebyshev_polynomial_w(input: Tensor, n, *, out=None) → Tensor

Chebyshev polynomial of the first kind $W_{n}\left(\text{input}\right)$.

Shifted Chebyshev Polynomials

• shifted_chebyshev_polynomial_t(input: Tensor, n, *, out=None) → Tensor

Shifted Chebyshev polynomial of the first kind $T_{n}^{\ast}\left(\text{input}\right)$.

• shifted_chebyshev_polynomial_u(input: Tensor, n, *, out=None) → Tensor

Shifted Chebyshev polynomial of the first kind $U_{n}^{\ast}\left(\text{input}\right)$.

• shifted_chebyshev_polynomial_v(input: Tensor, n, *, out=None) → Tensor

Shifted Chebyshev polynomial of the first kind $V_{n}^{\ast}\left(\text{input}\right)$.

• shifted_chebyshev_polynomial_w(input: Tensor, n, *, out=None) → Tensor

Shifted Chebyshev polynomial of the first kind $W_{n}^{\ast}\left(\text{input}\right)$.

Hermite Polynomials

• hermite_polynomial_h(input: Tensor, n, *, out=None) → Tensor

Physicist’s Hermite polynomial $H_{n}\left(\text{input}\right)$.

• hermite_polynomial_he(input: Tensor, n, *, out=None) → Tensor

Probabilist’s Hermite polynomial $He_{n}\left(\text{input}\right)$.

Charlier Polynomials

• charlier_polynomial_c(input: Tensor, a, n, *, out=None) → Tensor

Gegenbauer Polynomials

• gegenbauer_polynomial_c(input: Tensor, m, n, *, out=None) → Tensor

Gegenbauer polynomial $C_{n}\left(\text{input}\right)$.

Jacobi Polynomials

• jacobi_polynomial_p(input: Tensor, a, b, n, *, out=None) → Tensor

Jacobi polynomial $P_{n}\left(\text{input}\right)$.

Laguerre Polynomials

• generalized_laguerre_polynomial_l(input: Tensor, a, n, *, out=None) → Tensor

• laguerre_polynomial_l(input: Tensor, n, *, out=None) → Tensor

Legendre Polynomials

• legendre_polynomial_p(input: Tensor, n, *, out=None) → Tensor

Legendre polynomial $P_{n}\left(\text{input}\right)$.

Shifted Legendre Polynomials

• shifted_legendre_polynomial_p(input: Tensor, n, *, out=None) → Tensor

Shifted Legendre polynomial $P_{n}^{\ast}\left(\text{input}\right)$.