Content-Length: 92406 | pFad | https://dlmf.nist.gov/././bib/../././././././.././bib/../././././././././././bib/../././././18.4#F1

DLMF: §18.4 Graphics ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

About the Project

18 Orthogonal Polynomials Classical Orthogonal Polynomials 18.3 Definitions 18.5 Explicit Representations

§18.4 Graphics

ⓘ

Permalink:: http://dlmf.nist.gov/18.4
See also:: Annotations for Ch.18

Contents

§18.4(i) Graphs

ⓘ

Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/18.4.i
See also:: Annotations for §18.4 and Ch.18

See accompanying text — Figure 18.4.1: Jacobi polynomials $P^{(1.5,-0.5)}_{n}\left(x\right)$ , $n=1,2,3,4,5$ . Magnify

See accompanying text — Figure 18.4.2: Jacobi polynomials $P^{(1.25,0.75)}_{n}\left(x\right)$ , $n=7,8$ . This illustrates inequalities for extrema of a Jacobi polynomial; see (18.14.16). See also Askey (1990). Magnify

See accompanying text — Figure 18.4.2: Jacobi polynomials $P^{(1.25,0.75)}_{n}\left(x\right)$ , $n=7,8$ . This illustrates inequalities for extrema of a Jacobi polynomial; see (18.14.16). See also Askey (1990). Magnify

See accompanying text — Figure 18.4.4: Legendre polynomials $P_{n}\left(x\right)$ , $n=1,2,3,4,5$ . Magnify

See accompanying text — Figure 18.4.4: Legendre polynomials $P_{n}\left(x\right)$ , $n=1,2,3,4,5$ . Magnify

See accompanying text — Figure 18.4.6: Laguerre polynomials $L^{(\alpha)}_{3}\left(x\right)$ , $\alpha=0,1,2,3,4$ . Magnify

See accompanying text — Figure 18.4.6: Laguerre polynomials $L^{(\alpha)}_{3}\left(x\right)$ , $\alpha=0,1,2,3,4$ . Magnify

§18.4(ii) Surfaces

ⓘ

Notes:: These surfaces were produced at NIST.
Permalink:: http://dlmf.nist.gov/18.4.ii
See also:: Annotations for §18.4 and Ch.18

See accompanying text — Figure 18.4.8: Laguerre polynomials $L^{(\alpha)}_{3}\left(x\right)$ , $0\leq\alpha\leq 3$ , $0\leq x\leq 10$ . Magnify 3D Help

See accompanying text — Figure 18.4.8: Laguerre polynomials $L^{(\alpha)}_{3}\left(x\right)$ , $0\leq\alpha\leq 3$ , $0\leq x\leq 10$ . Magnify 3D Help

18.3 Definitions 18.5 Explicit Representations

© 2010–2024 NIST / Disclaimer / Feedback; Version 1.2.3; Release date 2024-12-15.

NIST

Site Privacy Accessibility Privacy Program Copyrights Vulnerability Disclosure No Fear Act Policy FOIA Environmental Policy Scientific Integrity Information Quality Standards Commerce.gov Science.gov USA.gov