Content-Length: 175784 | pFad | https://dlmf.nist.gov/./../././.././././././front/../././10.3.F11

6000 DLMF: §10.3 Graphics ‣ Bessel and Hankel Functions ‣ Chapter 10 Bessel Functions

About the Project

10 Bessel Functions Bessel and Hankel Functions 10.2 Definitions 10.4 Connection Formulas

§10.3 Graphics

ⓘ

Keywords:: Bessel functions, graphics
Permalink:: http://dlmf.nist.gov/10.3
See also:: Annotations for Ch.10

Contents

§10.3(i) Real Order and Variable

ⓘ

Keywords:: Bessel functions, graphics, modulus and phase functions
Notes:: These graphics were produced at NIST.
Referenced by:: §10.74(vi)
Permalink:: http://dlmf.nist.gov/10.3.i
See also:: Annotations for §10.3 and Ch.10

For the modulus and phase functions $M_{\nu}\left(x\right)$ , $\theta_{\nu}\left(x\right)$ , $N_{\nu}\left(x\right)$ , and $\phi_{\nu}\left(x\right)$ see §10.18.

See accompanying text — Figure 10.3.1: $J_{0}\left(x\right)$ , $Y_{0}\left(x\right)$ , $J_{1}\left(x\right)$ , $Y_{1}\left(x\right)$ , $0\leq x\leq 10$ . Magnify

See accompanying text — Figure 10.3.1: $J_{0}\left(x\right)$ , $Y_{0}\left(x\right)$ , $J_{1}\left(x\right)$ , $Y_{1}\left(x\right)$ , $0\leq x\leq 10$ . Magnify

See accompanying text — Figure 10.3.3: $J_{5}'\left(x\right)$ , $Y_{5}'\left(x\right)$ , $N_{5}\left(x\right)$ , $0\leq x\leq 15$ . Magnify

See accompanying text — Figure 10.3.3: $J_{5}'\left(x\right)$ , $Y_{5}'\left(x\right)$ , $N_{5}\left(x\right)$ , $0\leq x\leq 15$ . Magnify

See accompanying text — Figure 10.3.5: $J_{\nu}\left(x\right)$ , $0\leq x\leq 10$ , $0\leq\nu\leq 5$ . Magnify 3D Help

See accompanying text — Figure 10.3.5: $J_{\nu}\left(x\right)$ , $0\leq x\leq 10$ , $0\leq\nu\leq 5$ . Magnify 3D Help

See accompanying text — Figure 10.3.7: $J_{\nu}'\left(x\right)$ , $0\leq x\leq 10$ , $0\leq\nu\leq 5$ . Magnify 3D Help

See accompanying text — Figure 10.3.7: $J_{\nu}'\left(x\right)$ , $0\leq x\leq 10$ , $0\leq\nu\leq 5$ . Magnify 3D Help

§10.3(ii) Real Order, Complex Variable

ⓘ

Keywords:: Hankel functions, graphics
Notes:: These graphics were produced at NIST.
Referenced by:: §10.26(ii), §10.74(vi)
Permalink:: http://dlmf.nist.gov/10.3.ii
See also:: Annotations for §10.3 and Ch.10

In the graphics shown in this subsection, height corresponds to the absolute value of the function and color to the phase. See also p. About Color Map.

See accompanying text — Figure 10.3.9: $J_{0}\left(x+iy\right)$ , $-10\leq x\leq 10$ , $-4\leq y\leq 4$ . Magnify 3D Help

See accompanying text — Figure 10.3.9: $J_{0}\left(x+iy\right)$ , $-10\leq x\leq 10$ , $-4\leq y\leq 4$ . Magnify 3D Help

See accompanying text — Figure 10.3.11: $J_{1}\left(x+iy\right)$ , $-10\leq x\leq 10$ , $-4\leq y\leq 4$ . Magnify 3D Help

See accompanying text — Figure 10.3.11: $J_{1}\left(x+iy\right)$ , $-10\leq x\leq 10$ , $-4\leq y\leq 4$ . Magnify 3D Help

See accompanying text — Figure 10.3.13: $J_{5}\left(x+iy\right)$ , $-10\leq x\leq 10$ , $-4\leq y\leq 4$ . Magnify 3D Help

See accompanying text — Figure 10.3.13: $J_{5}\left(x+iy\right)$ , $-10\leq x\leq 10$ , $-4\leq y\leq 4$ . Magnify 3D Help

See accompanying text — Figure 10.3.15: $J_{5.5}\left(x+iy\right)$ , $-10\leq x\leq 10$ , $-4\leq y\leq 4$ . Principal value. There is a cut along the negative real axis. Magnify 3D Help

See accompanying text — Figure 10.3.15: $J_{5.5}\left(x+iy\right)$ , $-10\leq x\leq 10$ , $-4\leq y\leq 4$ . Principal value. There is a cut along the negative real axis. Magnify 3D Help

§10.3(iii) Imaginary Order, Real Variable

ⓘ

Keywords:: Bessel functions, graphics, graphs, of imaginary order
Notes:: These graphs were produced at NIST.
Referenced by:: §10.24
Permalink:: http://dlmf.nist.gov/10.3.iii
See also:: Annotations for §10.3 and Ch.10

For the notation see §10.24.

See accompanying text — Figure 10.3.17: $\widetilde{J}_{1/2}\left(x\right)$ , $\widetilde{Y}_{1/2}\left(x\right)$ , $0.01\leq x\leq 10$ . Magnify

See accompanying text — Figure 10.3.17: $\widetilde{J}_{1/2}\left(x\right)$ , $\widetilde{Y}_{1/2}\left(x\right)$ , $0.01\leq x\leq 10$ . Magnify

See accompanying text — Figure 10.3.19: $\widetilde{J}_{5}\left(x\right)$ , $\widetilde{Y}_{5}\left(x\right)$ , $0.01\leq x\leq 10$ . Magnify

10.2 Definitions 10.4 Connection Formulas

© 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