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

§10.48 Graphs

Notes:: These graphs were produced at NIST.
Keywords:: spherical Bessel functions
Permalink:: http://dlmf.nist.gov/10.48

Figure 10.48.1: $\mathop{\mathsf{j}_{{n}}\/}\nolimits\!\left(x\right),n=0(1)4,$ $0\leq x\leq 12$ .

Symbols:: $\mathop{\mathsf{j}_{{n}}\/}\nolimits\!\left(z\right)$ : spherical Bessel function of the first kind, : integer and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F1
Encodings:: pdf, png

Figure 10.48.2: $\mathop{\mathsf{y}_{{n}}\/}\nolimits\!\left(x\right),n=0(1)4,$ $0<x\leq 12$ .

Symbols:: $\mathop{\mathsf{y}_{{n}}\/}\nolimits\!\left(z\right)$ : spherical Bessel function of the second kind, : integer and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F2
Encodings:: pdf, png

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

Symbols:: $\mathop{\mathsf{j}_{{n}}\/}\nolimits\!\left(z\right)$ : spherical Bessel function of the first kind, $\mathop{\mathsf{y}_{{n}}\/}\nolimits\!\left(z\right)$ : spherical Bessel function of the second kind and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F3
Encodings:: pdf, png

Figure 10.48.4: ${\mathop{\mathsf{j}_{{5}}\/}\nolimits^{{\prime}}}\!\left(x\right)$ , ${\mathop{\mathsf{y}_{{5}}\/}\nolimits^{{\prime}}}\!\left(x\right)$ , $\sqrt{{{\mathop{\mathsf{j}_{{5}}\/}\nolimits^{{\prime}}}^{{2}}}\!\left(x\right% )+{{\mathop{\mathsf{y}_{{5}}\/}\nolimits^{{\prime}}}^{{2}}}\!\left(x\right)}$ , $0\leq x\leq 12$ .

Symbols:: $\mathop{\mathsf{j}_{{n}}\/}\nolimits\!\left(z\right)$ : spherical Bessel function of the first kind, $\mathop{\mathsf{y}_{{n}}\/}\nolimits\!\left(z\right)$ : spherical Bessel function of the second kind and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F4
Encodings:: pdf, png

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

Symbols:: $\mathop{{\mathsf{i}^{{(1)}}_{{n}}}\/}\nolimits\!\left(z\right)$ : modified spherical Bessel function, $\mathop{{\mathsf{i}^{{(2)}}_{{n}}}\/}\nolimits\!\left(z\right)$ : modified spherical Bessel function, $\mathop{\mathsf{k}_{{n}}\/}\nolimits\!\left(z\right)$ : modified spherical Bessel function and : real variable
Referenced by:: 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

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

Symbols:: $\mathop{{\mathsf{i}^{{(1)}}_{{n}}}\/}\nolimits\!\left(z\right)$ : modified spherical Bessel function, $\mathop{{\mathsf{i}^{{(2)}}_{{n}}}\/}\nolimits\!\left(z\right)$ : modified spherical Bessel function, $\mathop{\mathsf{k}_{{n}}\/}\nolimits\!\left(z\right)$ : modified spherical Bessel function and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F6
Encodings:: pdf, png

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

Symbols:: $\mathop{{\mathsf{i}^{{(1)}}_{{n}}}\/}\nolimits\!\left(z\right)$ : modified spherical Bessel function, $\mathop{{\mathsf{i}^{{(2)}}_{{n}}}\/}\nolimits\!\left(z\right)$ : modified spherical Bessel function, $\mathop{\mathsf{k}_{{n}}\/}\nolimits\!\left(z\right)$ : modified spherical Bessel function and : real variable
Permalink:: http://dlmf.nist.gov/10.48.F7
Encodings:: pdf, png

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