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NIST
10
Bessel Functions
Bessel and Hankel Functions
10.9
Integral Representations
10.11
Analytic Continuation
§10.10
Continued Fractions
ⓘ
Keywords:
Bessel functions
,
continued fractions
Notes:
See
Watson (
1944
, §§5.6, 9.65)
.
Referenced by:
§3.10(ii)
Permalink:
http://dlmf.nist.gov/10.10
See also:
Annotations for
Ch.10
Assume
J
ν
-
1
(
z
)
≠
0
. Then
10.10.1
J
ν
(
z
)
J
ν
-
1
(
z
)
=
1
2
ν
z
-
1
-
1
2
(
ν
+
1
)
z
-
1
-
1
2
(
ν
+
2
)
z
-
1
-
⋯
,
z
≠
0
,
ⓘ
Symbols:
J
ν
(
z
)
: Bessel function of the first kind
,
z
: complex variable
and
ν
: complex parameter
A&S Ref:
9.1.73
Referenced by:
§10.33
,
§10.74(v)
Permalink:
http://dlmf.nist.gov/10.10.E1
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
§10.10
and
Ch.10
10.10.2
J
ν
(
z
)
J
ν
-
1
(
z
)
=
1
2
z
/
ν
1
-
1
4
z
2
/
(
ν
(
ν
+
1
)
)
1
-
1
4
z
2
/
(
(
ν
+
1
)
(
ν
+
2
)
)
1
-
⋯
,
ν
≠
0
,
-
1
,
-
2
,
…
.
ⓘ
Symbols:
J
ν
(
z
)
: Bessel function of the first kind
,
z
: complex variable
and
ν
: complex parameter
A&S Ref:
9.1.73
Referenced by:
§10.33
,
§10.74(v)
Permalink:
http://dlmf.nist.gov/10.10.E2
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
§10.10
and
Ch.10
See also
Cuyt
et al.
(
2008
, pp. 349–356)
.