§10.62 Graphs

Notes:: These graphs were produced at NIST.
Keywords:: Kelvin functions
Permalink:: http://dlmf.nist.gov/10.62

For the modulus functions $\mathop{M\/}\nolimits\!\left(x\right)$ and $\mathop{N\/}\nolimits\!\left(x\right)$ see §10.68(i) with $\nu=0$ .

Figure 10.62.1: $\mathop{\mathrm{ber}\/}\nolimits x,\mathop{\mathrm{bei}\/}\nolimits x,{\mathop{\mathrm{ber}\/}\nolimits^{{\prime}}}x,{\mathop{\mathrm{bei}\/}\nolimits^{{\prime}}}x,$ $0\leq x\leq 8$ .

Symbols:: $\mathop{\mathrm{bei}_{{\nu}}\/}\nolimits\!\left(x\right)$ : Kelvin function, $\mathop{\mathrm{ber}_{{\nu}}\/}\nolimits\!\left(x\right)$ : Kelvin function and $x$ : real variable
Permalink:: http://dlmf.nist.gov/10.62.F1
Encodings:: pdf, png

Figure 10.62.2: $\mathop{\mathrm{ker}\/}\nolimits x,\mathop{\mathrm{kei}\/}\nolimits x,{\mathop{\mathrm{ker}\/}\nolimits^{{\prime}}}x,{\mathop{\mathrm{kei}\/}\nolimits^{{\prime}}}x,$ $0\leq x\leq 8$ .

Symbols:: $\mathop{\mathrm{kei}_{{\nu}}\/}\nolimits\!\left(x\right)$ : Kelvin function, $\mathop{\mathrm{ker}_{{\nu}}\/}\nolimits\!\left(x\right)$ : Kelvin function and $x$ : real variable
Permalink:: http://dlmf.nist.gov/10.62.F2
Encodings:: pdf, png

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

Symbols:: $\mathop{\mathrm{bei}_{{\nu}}\/}\nolimits\!\left(x\right)$ : Kelvin function, $\mathop{\mathrm{ber}_{{\nu}}\/}\nolimits\!\left(x\right)$ : Kelvin function, $e$ : base of exponential function, $\mathop{M_{{\nu}}\/}\nolimits\!\left(x\right)$ : modulus of Bessel functions and $x$ : real variable
Permalink:: http://dlmf.nist.gov/10.62.F3
Encodings:: pdf, png

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

Symbols:: $\mathop{\mathrm{kei}_{{\nu}}\/}\nolimits\!\left(x\right)$ : Kelvin function, $\mathop{\mathrm{ker}_{{\nu}}\/}\nolimits\!\left(x\right)$ : Kelvin function, $e$ : base of exponential function, $\mathop{N_{{\nu}}\/}\nolimits\!\left(x\right)$ : modulus of derivatives of Bessel functions and $x$ : real variable
Permalink:: http://dlmf.nist.gov/10.62.F4
Encodings:: pdf, png