10 Bessel Functions Spherical Bessel Functions 10.47 Definitions and Basic Properties 10.49 Explicit Formulas

§10.48 Graphs

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Keywords:: graphs, spherical Bessel functions
Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/10.48
See also:: Annotations for Ch.10

Figure 10.48.1: $\mathsf{j}_{n}\left(x\right)$ ,

, $0\leq x\leq 12$ . Magnify

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Symbols:: $\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)$ : spherical Bessel function of the first kind, : integer and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F1
Encodings:: pdf, png
See also:: Annotations for §10.48 and Ch.10

Figure 10.48.2: $\mathsf{y}_{n}\left(x\right)$ ,

, $0<x\leq 12$ . Magnify

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Symbols:: $\mathsf{y}_{\NVar{n}}\left(\NVar{z}\right)$ : spherical Bessel function of the second kind, : integer and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F2
Encodings:: pdf, png
See also:: Annotations for §10.48 and Ch.10

Figure 10.48.3: $\mathsf{j}_{5}\left(x\right)$ , $\mathsf{y}_{5}\left(x\right)$ , $\sqrt{{\mathsf{j}_{5}}^{2}\left(x\right)+{\mathsf{y}_{5}}^{2}\left(x\right)}$ , $0\leq x\leq 12$ . Magnify

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Symbols:: $\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)$ : spherical Bessel function of the first kind, $\mathsf{y}_{\NVar{n}}\left(\NVar{z}\right)$ : spherical Bessel function of the second kind and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F3
Encodings:: pdf, png
See also:: Annotations for §10.48 and Ch.10

Figure 10.48.4: $\mathsf{j}_{5}'\left(x\right)$ , $\mathsf{y}_{5}'\left(x\right)$ , $\sqrt{{\mathsf{j}_{5}'}^{2}\left(x\right)+{\mathsf{y}_{5}'}^{2}\left(x\right)}$ , $0\leq x\leq 12$ . Magnify

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Symbols:: $\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)$ : spherical Bessel function of the first kind, $\mathsf{y}_{\NVar{n}}\left(\NVar{z}\right)$ : spherical Bessel function of the second kind and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F4
Encodings:: pdf, png
See also:: Annotations for §10.48 and Ch.10

Figure 10.48.5: ${\mathsf{i}^{(1)}_{0}}\left(x\right)$ , ${\mathsf{i}^{(2)}_{0}}\left(x\right)$ , $\mathsf{k}_{0}\left(x\right)$ , $0\leq x\leq 4$ . Magnify

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Symbols:: ${\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)$ : modified spherical Bessel function, ${\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)$ : modified spherical Bessel function, $\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)$ : modified spherical Bessel function and : real variable
Referenced by:: Erratum (V1.0.1) for Figure 10.48.5
Permalink:: http://dlmf.nist.gov/10.48.F5
Encodings:: pdf, png
Errata (effective with 1.0.1):: The ordinate labels 2 and 4 originally were misplaced at ordinates 3 and 5.
Reported 2010-11-08 by Wolfgang Ehrhardt
See also:: Annotations for §10.48 and Ch.10

Figure 10.48.6: ${\mathsf{i}^{(1)}_{1}}\left(x\right),{\mathsf{i}^{(2)}_{1}}\left(x\right),% \mathsf{k}_{1}\left(x\right)$ , $0\leq x\leq 4$ . Magnify

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Symbols:: ${\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)$ : modified spherical Bessel function, ${\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)$ : modified spherical Bessel function, $\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)$ : modified spherical Bessel function and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F6
Encodings:: pdf, png
See also:: Annotations for §10.48 and Ch.10

Figure 10.48.7: ${\mathsf{i}^{(1)}_{5}}\left(x\right)$ , ${\mathsf{i}^{(2)}_{5}}\left(x\right)$ , $\mathsf{k}_{5}\left(x\right)$ , $0\leq x\leq 8$ . Magnify

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Symbols:: ${\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)$ : modified spherical Bessel function, ${\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)$ : modified spherical Bessel function, $\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)$ : modified spherical Bessel function and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F7
Encodings:: pdf, png
See also:: Annotations for §10.48 and Ch.10

10.47 Definitions and Basic Properties 10.49 Explicit Formulas

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