BESSELJ
Bessel J functions of noninteger order

BESSELJ is a FORTRAN90 library which evaluates Bessel J functions of noninteger order.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

BESSELJ is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

FN, a FORTRAN90 library which approximates elementary and special functions using Chebyshev polynomials; functions include Airy, Bessel I, J, K and Y, beta, confluent hypergeometric, error, gamma, log gamma, Pochhammer, Spence; integrals include hyperbolic cosine, cosine, Dawson, exponential, logarithmic, hyperbolic sine, sine; by Wayne Fullerton.

SPECFUN, a FORTRAN90 library which computes special functions, including Bessel I, J, K and Y functions, and the Dawson, E1, EI, Erf, Gamma, log Gamma, Psi/Digamma functions, by William Cody and Laura Stoltz;

SPECIAL_FUNCTIONS, a FORTRAN90 library which computes the Beta, Error, Gamma, Lambda, Psi functions, the Airy, Bessel I, J, K and Y, Hankel, Jacobian elliptic, Kelvin, Mathieu, Struve functions, spheroidal angular functions, parabolic cylinder functions, hypergeometric functions, the Bernoulli and Euler numbers, the Hermite, Laguerre and Legendre polynomials, the cosine, elliptic, exponential, Fresnel and sine integrals, by Shanjie Zhang, Jianming Jin;

TOMS715, a FORTRAN90 library which evaluates special functions, including the Bessel I, J, K, and Y functions of order 0, of order 1, and of any real order, Dawson's integral, the error function, exponential integrals, the gamma function, the normal distribution function, the psi function. This is a version of ACM TOMS algorithm 715.

Reference:

1. Donald Amos, SL Daniel, MK Weston,
   CDC 6600 subroutines IBESS and JBESS for Bessel functions I(NU,X) and J(NU,X),
   ACM Transactions on Mathematical Software,
   Volume 3, Number 1, March 1977, pages 76-92.
2. William Cody,
   Algorithm 715: SPECFUN - A Portable FORTRAN Package of Special Function Routines and Test Drivers,
   ACM Transactions on Mathematical Software,
   Volume 19, Number 1, March 1993, pages 22-32.

Source Code:

• besselj.f90, the source code.

Examples and Tests:

• besselj_test.f90, a sample calling program.
• besselj_test.txt, the output file.

List of Routines:

• BESSEL_JX_VALUES returns some values of the Jx Bessel function.
• DBESJ computes Bessel J functions of non integer order.
• D1MACH returns double precision real machine constants.
• D9LGMC computes the log Gamma correction factor.
• DASYJY computes Bessel J and Y functions of large order.
• DCSEVL evaluates a Chebyshev series.
• DJAIRY computes the Airy function Ai(x) and its derivative.
• DGAMLM computes bounds for the argument in the Gamma function.
• DGAMMA computes the complete Gamma function.
• DLNGAM computes the logarithm of the absolute value of the Gamma function.
• I1MACH returns integer machine constants.
• INITDS determines the necessary length of a Chebyshev series.
• RJBESL evaluates a sequence of Bessel J functions.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• XERMSG processes error messages.

You can go up one level to the FORTRAN90 source codes.