Last Updated：2025/11/21
(mathematics) Any of class of special functions, usually denoted as two pairs of functions berₙ(x), beiₙ(x), kerₙ(x) and keiₙ(x) with variable x and given order number n. The former two functions berₙ(x) and beiₙ(x) respectively correspond to the real part and the imaginary part of the Kelvin differential equation's solution that can be expressed with the Bessel function of the first kind Jₙ(x), and the latter kerₙ(x) and keiₙ(x) correspond to those that can be expressed with the modified Bessel function of the second kind Kₙ(x).
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Kelvin function
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Source Word
Kelvin function
Noun
(mathematics)
Any
of
class
of
special
functions,
usually
denoted
as
two
pairs
of
functions
berₙ(x),
beiₙ(x),
kerₙ(x)
and
keiₙ(x)
with
variable
x
and
given
order
number
n.
The
former
two
functions
berₙ(x)
and
beiₙ(x)
respectively
correspond
to
the
real
part
and
the
imaginary
part
of
the
Kelvin
differential
equation's
solution
that
can
be
expressed
with
the
Bessel
function
of
the
first
kind
Jₙ(x),
and
the
latter
kerₙ(x)
and
keiₙ(x)
correspond
to
those
that
can
be
expressed
with
the
modified
Bessel
function
of
the
second
kind
Kₙ(x).
Japanese Meaning
数学における特殊関数の一群で、通常は2組の関数 berₙ(x), beiₙ(x) および kerₙ(x), keiₙ(x) により表される。前者の berₙ(x) と beiₙ(x) は、Kelvin微分方程式の解（第一種Bessel関数 Jₙ(x) を用いて表現できる）の実部と虚部にそれぞれ対応し、後者の kerₙ(x) と keiₙ(x) は、第二種修正Bessel関数 Kₙ(x) を用いて表現できるものに対応する。
Sense（1）
(mathematics)
Any
of
class
of
special
functions,
usually
denoted
as
two
pairs
of
functions
berₙ(x),
beiₙ(x),
kerₙ(x)
and
keiₙ(x)
with
variable
x
and
given
order
number
n.
The
former
two
functions
berₙ(x)
and
beiₙ(x)
respectively
correspond
to
the
real
part
and
the
imaginary
part
of
the
Kelvin
differential
equation's
solution
that
can
be
expressed
with
the
Bessel
function
of
the
first
kind
Jₙ(x),
and
the
latter
kerₙ(x)
and
keiₙ(x)
correspond
to
those
that
can
be
expressed
with
the
modified
Bessel
function
of
the
second
kind
Kₙ(x).
（ plural ）
