Cylindrical Bessel functions of integral order.
Stephen L. Moshier (original C code). Conversion to D by Don Clugston
- real cylBessel_j0(real x) ¶
-
Bessel function of order zero
Returns Bessel function of first kind, order zero of the argument.
- real cylBessel_y0(real x) ¶
-
Bessel function of the second kind, order zero
Also known as the cylindrical Neumann function, order zero.
Returns Bessel function of the second kind, of order
zero, of the argument.
- real cylBessel_j1(real x) ¶
-
Bessel function of order one
Returns Bessel function of order one of the argument.
- real cylBessel_y1(real x) ¶
-
Bessel function of the second kind, order zero
Returns Bessel function of the second kind, of order
zero, of the argument.
- real cylBessel_jn(int n, real x) ¶
-
Bessel function of integer order
Returns Bessel function of order n, where n is a
(possibly negative) integer.
The ratio of jn(x) to j0(x) is computed by backward
recurrence. First the ratio jn/jn-1 is found by a
continued fraction expansion. Then the recurrence
relating successive orders is applied until j0 or j1 is
reached.
If n = 0 or 1 the routine for j0 or j1 is called
directly.
Not suitable for large n or x.
- real cylBessel_yn(int n, real x) ¶
-
Bessel function of second kind of integer order
Returns Bessel function of order n, where n is a
(possibly negative) integer.
The function is evaluated by forward recurrence on
n, starting with values computed by the routines
cylBessel_y0() and cylBessel_y1().
If n = 0 or 1 the routine for cylBessel_y0 or cylBessel_y1 is called
directly.
- double cylBessel_i0(double x) ¶
-
Modified Bessel function of order zero
Returns modified Bessel function of order zero of the
argument.
The function is defined as i0(x) = j0( ix ).
The range is partitioned into the two intervals [0,8] and
(8, infinity). Chebyshev polynomial expansions are employed
in each interval.
- double cylBessel_i1(double x) ¶
-
Modified Bessel function of order one
Returns modified Bessel function of order one of the
argument.
The function is defined as i1(x) = -i j1( ix ).
The range is partitioned into the two intervals [0,8] and
(8, infinity). Chebyshev polynomial expansions are employed
in each interval.