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10
Bessel Functions
Kelvin Functions
10.61
Definitions and Basic Properties
10.63
Recurrence Relations and Derivatives
§10.62
Graphs
Notes:
These graphs were produced at NIST.
Keywords:
Kelvin functions
Permalink:
http://dlmf.nist.gov/10.62
For the modulus functions
$M\left(x\right)$
and
$N\left(x\right)$
see §
10.68(i)
with
$\nu =0$
.
Figure 10.62.1:
$\mathrm{ber}x$
,
$\mathrm{bei}x$
,
${\mathrm{ber}}^{\prime}x$
,
${\mathrm{bei}}^{\prime}x$
,
$0\le x\le 8$
.
Symbols:
${\mathrm{bei}}_{\nu}\left(x\right)$
: Kelvin function
,
${\mathrm{ber}}_{\nu}\left(x\right)$
: Kelvin function
and
$x$
: real variable
Permalink:
http://dlmf.nist.gov/10.62.F1
Encodings:
pdf
,
png
Figure 10.62.2:
$\mathrm{ker}x$
,
$\mathrm{kei}x$
,
${\mathrm{ker}}^{\prime}x$
,
${\mathrm{kei}}^{\prime}x$
,
$0\le x\le 8$
.
Symbols:
${\mathrm{kei}}_{\nu}\left(x\right)$
: Kelvin function
,
${\mathrm{ker}}_{\nu}\left(x\right)$
: Kelvin function
and
$x$
: real variable
Permalink:
http://dlmf.nist.gov/10.62.F2
Encodings:
pdf
,
png
Figure 10.62.3:
${\mathrm{e}}^{-x/\sqrt{2}}\mathrm{ber}x$
,
${\mathrm{e}}^{-x/\sqrt{2}}\mathrm{bei}x$
,
${\mathrm{e}}^{-x/\sqrt{2}}M\left(x\right)$
,
$0\le x\le 8$
.
Symbols:
${\mathrm{bei}}_{\nu}\left(x\right)$
: Kelvin function
,
${\mathrm{ber}}_{\nu}\left(x\right)$
: Kelvin function
,
$\mathrm{e}$
: base of exponential function
,
${M}_{\nu}\left(x\right)$
: modulus of Bessel functions
and
$x$
: real variable
Permalink:
http://dlmf.nist.gov/10.62.F3
Encodings:
pdf
,
png
Figure 10.62.4:
${\mathrm{e}}^{x/\sqrt{2}}\mathrm{ker}x$
,
${\mathrm{e}}^{x/\sqrt{2}}\mathrm{kei}x$
,
${\mathrm{e}}^{x/\sqrt{2}}N\left(x\right)$
,
$0\le x\le 8$
.
Symbols:
${\mathrm{kei}}_{\nu}\left(x\right)$
: Kelvin function
,
${\mathrm{ker}}_{\nu}\left(x\right)$
: Kelvin function
,
$\mathrm{e}$
: base of exponential function
,
${N}_{\nu}\left(x\right)$
: modulus of derivatives of Bessel functions
and
$x$
: real variable
Permalink:
http://dlmf.nist.gov/10.62.F4
Encodings:
pdf
,
png