33 Coulomb Functions Variables $r,\epsilon$ 33.14 Definitions and Basic Properties 33.16 Connection Formulas

§33.15 Graphics

Keywords:: Coulomb functions: variables $r,\epsilon$
Permalink:: http://dlmf.nist.gov/33.15

§33.15(i) Line Graphs of the Coulomb Functions $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ and $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$
§33.15(ii) Surfaces of the Coulomb Functions $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ , $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ , $\mathop{s\/}\nolimits\!\left(\epsilon,\ell;r\right)$ , and $\mathop{c\/}\nolimits\!\left(\epsilon,\ell;r\right)$

§33.15(i) Line Graphs of the Coulomb Functions $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ and $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$

Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/33.15.i

Figure 33.15.1: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right),\mathop{h\/}\nolimits\!% \left(\epsilon,\ell;r\right)$ with $\ell=0,\epsilon=4$ .

Symbols:: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : regular Coulomb function, $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : irregular Coulomb function, $\ell$ : nonnegative integer, : real variable and $\epsilon$ : real parameter
Permalink:: http://dlmf.nist.gov/33.15.F1
Encodings:: pdf, png

Figure 33.15.2: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right),\mathop{h\/}\nolimits\!% \left(\epsilon,\ell;r\right)$ with $\ell=1,\epsilon=4$ .

Symbols:: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : regular Coulomb function, $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : irregular Coulomb function, $\ell$ : nonnegative integer, : real variable and $\epsilon$ : real parameter
Permalink:: http://dlmf.nist.gov/33.15.F2
Encodings:: pdf, png

Figure 33.15.3: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right),\mathop{h\/}\nolimits\!% \left(\epsilon,\ell;r\right)$ with $\ell=0,\epsilon=-1/\nu^{2},\nu=1.5$ .

Symbols:: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : regular Coulomb function, $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : irregular Coulomb function, $\ell$ : nonnegative integer, : real variable and $\epsilon$ : real parameter
Permalink:: http://dlmf.nist.gov/33.15.F3
Encodings:: pdf, png

Figure 33.15.4: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right),\mathop{h\/}\nolimits\!% \left(\epsilon,\ell;r\right)$ with $\ell=0,\epsilon=-1/\nu^{2},\nu=2$ .

Symbols:: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : regular Coulomb function, $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : irregular Coulomb function, $\ell$ : nonnegative integer, : real variable and $\epsilon$ : real parameter
Permalink:: http://dlmf.nist.gov/33.15.F4
Encodings:: pdf, png

Figure 33.15.5: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right),\mathop{h\/}\nolimits\!% \left(\epsilon,\ell;r\right)$ with $\ell=0,\epsilon=-1/\nu^{2},\nu=2.5$ .

Symbols:: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : regular Coulomb function, $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : irregular Coulomb function, $\ell$ : nonnegative integer, : real variable and $\epsilon$ : real parameter
Permalink:: http://dlmf.nist.gov/33.15.F5
Encodings:: pdf, png

§33.15(ii) Surfaces of the Coulomb Functions $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ , $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ , $\mathop{s\/}\nolimits\!\left(\epsilon,\ell;r\right)$ , and $\mathop{c\/}\nolimits\!\left(\epsilon,\ell;r\right)$

Notes:: These surfaces were produced at NIST.
Keywords:: Coulomb functions: variables $r,\epsilon$
Permalink:: http://dlmf.nist.gov/33.15.ii

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Figure 33.15.6: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ with $\ell=0,-2<\epsilon<2,-15<r<15$ .

Symbols:: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : regular Coulomb function, $\ell$ : nonnegative integer, : real variable and $\epsilon$ : real parameter
Permalink:: http://dlmf.nist.gov/33.15.F6
Encodings:: VRML, X3D, pdf, png

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Figure 33.15.7: $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ with $\ell=0,-2<\epsilon<2,-15<r<15$ .

Symbols:: $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : irregular Coulomb function, $\ell$ : nonnegative integer, : real variable and $\epsilon$ : real parameter
Permalink:: http://dlmf.nist.gov/33.15.F7
Encodings:: VRML, X3D, pdf, png

Visualization Help

Figure 33.15.8: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ with $\ell=1,-2<\epsilon<2,-15<r<15$ .

Symbols:: $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : regular Coulomb function, $\ell$ : nonnegative integer, : real variable and $\epsilon$ : real parameter
Permalink:: http://dlmf.nist.gov/33.15.F8
Encodings:: VRML, X3D, pdf, png

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Figure 33.15.9: $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ with $\ell=1,-2<\epsilon<2,-15<r<15$ .

Symbols:: $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : irregular Coulomb function, $\ell$ : nonnegative integer, : real variable and $\epsilon$ : real parameter
Permalink:: http://dlmf.nist.gov/33.15.F9
Encodings:: VRML, X3D, pdf, png

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Figure 33.15.10: $\mathop{s\/}\nolimits\!\left(\epsilon,\ell;r\right)$ with $\ell=0,-0.15<\epsilon<0.10,0<r<65$ .

Symbols:: $\mathop{s\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : regular Coulomb function, $\ell$ : nonnegative integer, : real variable and $\epsilon$ : real parameter
Permalink:: http://dlmf.nist.gov/33.15.F10
Encodings:: VRML, X3D, pdf, png

Visualization Help

Figure 33.15.11: $\mathop{c\/}\nolimits\!\left(\epsilon,\ell;r\right)$ with $\ell=0,-0.15<\epsilon<0.10,0<r<65$ .

Symbols:: $\mathop{c\/}\nolimits\!\left(\epsilon,\ell;r\right)$ : irregular Coulomb function, $\ell$ : nonnegative integer, : real variable and $\epsilon$ : real parameter
Permalink:: http://dlmf.nist.gov/33.15.F11
Encodings:: VRML, X3D, pdf, png

© 2010–2013 NIST / Privacy Policy / Disclaimer / Feedback; Version 1.0.6; Release date 2013-05-06 Math-Image version (See MathML) . A Printed Companionis available. 33.14 Definitions and Basic Properties 33.16 Connection Formulas

§33.15 Graphics

Contents

§33.15(i) Line Graphs of the Coulomb Functions and

§33.15(ii) Surfaces of the Coulomb Functions , , , and

§33.15(i) Line Graphs of the Coulomb Functions $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ and $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$

§33.15(ii) Surfaces of the Coulomb Functions $\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ , $\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ , $\mathop{s\/}\nolimits\!\left(\epsilon,\ell;r\right)$ , and $\mathop{c\/}\nolimits\!\left(\epsilon,\ell;r\right)$