# HP F2226A - 48GII Graphic Calculator User Manual Page 534

Graphing calculator.

If you want to obtain an expression for J
use J(x,0,5). The result is
'1-0.25*x^3+0.015625*x^4-4.3403777E-4*x^6+6.782168E-6*x^8-
For non-integer values ν, the solution to the Bessel equation is given by
For integer values, the functions Jn(x) and J-n(x) are linearly dependent, since
therefore, we cannot use them to obtain a general function to the equation.
Instead, we introduce the Bessel functions of the second kind defined as
Y
ν
for non-integer ν, and for n integer, with n > 0, by
2
Y
(
x
)
J
(
x
)
n
n
π
where γ is the Euler constant, defined by
1
γ
lim
1 [
2
r
and h
represents the harmonic series
m
For the case n = 0, the Bessel function of the second kind is defined as
2
Y
(
x
)
0
π
(x) with, say, 5 terms in the series,
0
6.78168*x^10'.
⋅J
⋅J
y(x) = K
(x)+K
ν
ν
1
2
-
n
⋅J
J
(x) = (-1)
(x),
n
-n
(x) cos νπ – J
(x)]/sin νπ,
(x) = [J
ν
−ν
n
(
x
x
(ln
γ
)
2
π
m
0
n
x
(
n
m
1
)!
n
1
2
m
n
π
2
m
!
m
=
0
1
1
...
ln
r
]
3
r
1
1
h
=
1
+
+
+
...
m
2
3
x
J
(
x
)
(ln
γ
)
0
2
m
(x).
m
1
) 1
(
h
h
)
m
m
n
x
2
m
n
2
m
( !
m
n
)!
2
m
x
. 0
5772156649
0
...,
1
+
m
m
1
(
) 1
h
2
m
m
x
.
2
m
2
2
(
m
) !
0
Page 16-56
2
m