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10 Bessel Functions Kelvin Functions 10.61 Definitions and Basic Properties 10.63 Recurrence Relations and Derivatives

§10.62 Graphs

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Keywords:: Kelvin functions, graphs
Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/10.62
See also:: Annotations for Ch.10

For the modulus functions $M\left(x\right)$ and $N\left(x\right)$ see §10.68(i) with $\nu=0$ .

See accompanying text

Figure 10.62.1: $\operatorname{ber}x$ , $\operatorname{bei}x$ , $\operatorname{ber}'x$ , $\operatorname{bei}'x$ , $0\leq x\leq 8$ . Magnify

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Symbols:: $\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}\right)$ : Kelvin function, $\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}\right)$ : Kelvin function and : real variable
Permalink:: http://dlmf.nist.gov/10.62.F1
Encodings:: pdf, png
See also:: Annotations for §10.62 and Ch.10

See accompanying text

Figure 10.62.2: $\operatorname{ker}x$ , $\operatorname{kei}x$ , $\operatorname{ker}'x$ , $\operatorname{kei}'x$ , $0\leq x\leq 8$ . Magnify

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Symbols:: $\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}\right)$ : Kelvin function, $\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}\right)$ : Kelvin function and : real variable
Permalink:: http://dlmf.nist.gov/10.62.F2
Encodings:: pdf, png
See also:: Annotations for §10.62 and Ch.10

See accompanying text

Figure 10.62.3: $e^{-x/\sqrt{2}}\operatorname{ber}x$ , $e^{-x/\sqrt{2}}\operatorname{bei}x$ , $e^{-x/\sqrt{2}}M\left(x\right)$ , $0\leq x\leq 8$ . Magnify

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Symbols:: $\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}\right)$ : Kelvin function, $\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}\right)$ : Kelvin function, $\mathrm{e}$ : base of natural logarithm, $M_{\NVar{\nu}}\left(\NVar{x}\right)$ : modulus of Bessel functions and : real variable
Permalink:: http://dlmf.nist.gov/10.62.F3
Encodings:: pdf, png
See also:: Annotations for §10.62 and Ch.10

See accompanying text

Figure 10.62.4: $e^{x/\sqrt{2}}\operatorname{ker}x$ , $e^{x/\sqrt{2}}\operatorname{kei}x$ , $e^{x/\sqrt{2}}N\left(x\right)$ , $0\leq x\leq 8$ . Magnify

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Symbols:: $\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}\right)$ : Kelvin function, $\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}\right)$ : Kelvin function, $\mathrm{e}$ : base of natural logarithm, $N_{\NVar{\nu}}\left(\NVar{x}\right)$ : modulus of derivatives of Bessel functions and : real variable
Permalink:: http://dlmf.nist.gov/10.62.F4
Encodings:: pdf, png
See also:: Annotations for §10.62 and Ch.10

10.61 Definitions and Basic Properties 10.63 Recurrence Relations and Derivatives

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