Bessel Functions |
| Bessel Functions of the First and Second Kinds |
J0(z) Returns J0(z),
the zeroth order Bessel function of the first kind.
J1(z) Returns J1(z),
the first-order Bessel function of the first kind.
Jn(m, z) Returns Jm(z),
the mth-order Bessel function of the first kind.
Y0(z) Returns Y0(z),
the zeroth order Bessel function of the second kind.
Y1(z) Returns Y1(z),
the first-order Bessel function of the second kind.
Yn(m, z) Returns Ym(z),
the mth-order Bessel function of the second kind.
Scaled versions have a scale factor of exp(−|Im(z)|). Type .sc after the function name for the scaled function.
| Modified (Hyperbolic) Bessel Functions |
I0(z) Returns I0(z),
the zeroth order modified Bessel function of the first kind.
I1(z) Returns I1(z),
the first-order modified Bessel function of the first kind.
In(m, z) Returns Im(z),
the mth-order modified Bessel function of the first kind.
K0(z) Returns K0(z),
the zeroth order modified Bessel function of the second kind.
K1(z) Returns K1(z),
the first-order modified Bessel function of the second kind.
Kn(m, z) Returns Km(z),
the mth-order modified Bessel function of the second kind.
Scaled modified Bessels of the first kind (I) have a scale factor of exp(−|Re(z)|). Scaled modified Bessels of the second kind (K) have a scale factor of exp(z). Type .sc after the function name for the scaled function.
| Hankel Functions |
H1(m, z) Returns the Hankel function (Bessel function
of the third kind) of the first kind.
H2(m, z) Returns the Hankel function of the second kind.
H1 scaled version has a scale factor of exp(-z*i). H2 scaled version has a scale factor of exp(z*i). Type .sc after the function name for the scaled function.
| Airy Functions |
Ai(z) Returns the Airy function of the first kind.
DAi(z) Returns the first derivative of Ai(z).
Bi(z) Returns the Airy function of the second kind.
DBi(z) Returns the first derivative of Bi(z).
The scaled Ai and DAi functions have a scale factor of
| Bessel Kelvin Functions |
bei(m, x)
ber(m, x)
Returns the value of the imaginary and real Bessel Kelvin functions of order m, respectively. The argument x must be real, and m must be a non-negative integer.
| Spherical Bessel Functions |
js(m, z)
ys(m, z)
Returns the value of the spherical Bessel functions of the first and second kind, of order m, respectively. No scaled versions are available.
In each case, unless noted,