Content-Length: 246635 | pFad | https://dlmf.nist.gov/./././././././../././.././not/.././././././././././././../././14.4#iii.info

DLMF: §14.4 Graphics ‣ Real Arguments ‣ Chapter 14 Legendre and Related Functions

About the Project

14 Legendre and Related Functions Real Arguments 14.3 Definitions and Hypergeometric Representations 14.5 Special Values

§14.4 Graphics

ⓘ

Permalink:: http://dlmf.nist.gov/14.4
See also:: Annotations for Ch.14

Contents

§14.4(i) Ferrers Functions: 2D Graphs

ⓘ

Keywords:: Ferrers functions, graphics
Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/14.4.i
See also:: Annotations for §14.4 and Ch.14

See accompanying text — Figure 14.4.1: $\mathsf{P}^{0}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.1: $\mathsf{P}^{0}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.3: $\mathsf{P}^{-1/2}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.3: $\mathsf{P}^{-1/2}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.5: $\mathsf{P}^{-1}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.5: $\mathsf{P}^{-1}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.7: $\mathsf{P}^{-\mu}_{0}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.7: $\mathsf{P}^{-\mu}_{0}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.9: $\mathsf{P}^{-\mu}_{1/2}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.9: $\mathsf{P}^{-\mu}_{1/2}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.11: $\mathsf{P}^{-\mu}_{1}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.11: $\mathsf{P}^{-\mu}_{1}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

§14.4(ii) Ferrers Functions: 3D Surfaces

ⓘ

Keywords:: Ferrers functions, graphics
Notes:: These surfaces were produced at NIST.
Permalink:: http://dlmf.nist.gov/14.4.ii
See also:: Annotations for §14.4 and Ch.14

See accompanying text — Figure 14.4.13: $\mathsf{P}^{0}_{\nu}\left(x\right)$ , $0\leq\nu\leq 10,-1<x<1$ . Magnify 3D Help

See accompanying text — Figure 14.4.13: $\mathsf{P}^{0}_{\nu}\left(x\right)$ , $0\leq\nu\leq 10,-1<x<1$ . Magnify 3D Help

See accompanying text — Figure 14.4.15: $\mathsf{P}^{-\mu}_{0}\left(x\right)$ , $0\leq\mu\leq 10,-1<x<1$ . Magnify 3D Help

See accompanying text — Figure 14.4.15: $\mathsf{P}^{-\mu}_{0}\left(x\right)$ , $0\leq\mu\leq 10,-1<x<1$ . Magnify 3D Help

§14.4(iii) Associated Legendre Functions: 2D Graphs

ⓘ

Keywords:: associated Legendre functions, graphics
Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/14.4.iii
See also:: Annotations for §14.4 and Ch.14

See accompanying text — Figure 14.4.17: $P^{0}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.17: $P^{0}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.19: $P^{-1/2}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.19: $P^{-1/2}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.21: $P^{-1}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.21: $P^{-1}_{\nu}\left(x\right)$ , $\nu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.23: $P^{-\mu}_{0}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.23: $P^{-\mu}_{0}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.25: $P^{-\mu}_{1/2}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.25: $P^{-\mu}_{1/2}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.27: $P^{-\mu}_{1}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

See accompanying text — Figure 14.4.27: $P^{-\mu}_{1}\left(x\right)$ , $\mu=0,\tfrac{1}{2},1,2,4$ . Magnify

§14.4(iv) Associated Legendre Functions: 3D Surfaces

ⓘ

Keywords:: associated Legendre functions, graphics
Notes:: These surfaces were produced at NIST.
Permalink:: http://dlmf.nist.gov/14.4.iv
See also:: Annotations for §14.4 and Ch.14

See accompanying text — Figure 14.4.29: $P^{0}_{\nu}\left(x\right)$ , $0\leq\nu\leq 10$ , $1<x<10$ . Magnify 3D Help

See accompanying text — Figure 14.4.29: $P^{0}_{\nu}\left(x\right)$ , $0\leq\nu\leq 10$ , $1<x<10$ . Magnify 3D Help

See accompanying text — Figure 14.4.31: $P^{-\mu}_{0}\left(x\right)$ , $0\leq\mu\leq 10$ , $1<x<10$ . Magnify 3D Help

See accompanying text — Figure 14.4.31: $P^{-\mu}_{0}\left(x\right)$ , $0\leq\mu\leq 10$ , $1<x<10$ . Magnify 3D Help

14.3 Definitions and Hypergeometric Representations 14.5 Special Values

© 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