Digital Library of Mathematical Functions
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§10.77 Software


§10.77(i) Introduction

In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. Citations in bulleted lists refer to papers for which research software has been made available and can be downloaded via the Web. References to research software that is available in other ways is listed separately.

A more complete list of available software for computing these functions is found in the Software Index. For another listing of Web-accessible software for the functions in this chapter, see GAMS Class C10.

§10.77(ii) Bessel Functions–Real Argument and Integer or Half-Integer Order (including Spherical Bessel Functions)

  • Ardill and Moriarty (1978). Fortran.

  • Boisvert and Saunders (1992). Vectorized Fortran.

  • Cody (1993b). Fortran.

  • Coleman (1980). Fortran.

  • Hill (1981). Fortran.

  • Ratis and Fernández de Córdoba (1993). Fortran.

  • Segura et al. (1997). Fortran.

See also Börsch-Supan (1960), Fox et al. (1978), Oser (1960), and Wojcicki (1961).

§10.77(iii) Bessel Functions–Real Order and Argument

  • Amos et al. (1977). Fortran.

  • Barnett (1982). Fortran.

  • Brent (1978b). Fortran.

  • Campbell (1979). Fortran.

  • Cody (1983). Fortran.

  • Cody (1993b). Fortran.

  • Weider (1999). Fortran.

See also Gautschi (1964b), Matviyenko (1993), Piessens (1984b), and Temme (1975, 1976).

§10.77(iv) Bessel Functions–Integer or Half-Integer Order and Complex Arguments, including Kelvin Functions

  • Burrell (1974). Fortran.

  • du Toit (1993). Pascal.

See also Babushkina et al. (1988a, b), and Fox et al. (1978).

§10.77(v) Bessel Functions–Real Order and Complex Argument (including Hankel Functions)

  • Amos (1986). Fortran.

  • Campbell (1981). Fortran.

  • Thompson and Barnett (1987). Fortran.

§10.77(vi) Bessel Functions–Imaginary Order and Real Argument

  • Gil et al. (2004a). Fortran.

See also Fabijonas et al. (2003).

§10.77(vii) Bessel Functions–Complex Order and Real Argument

  • Kodama (2008). Fortran.

§10.77(viii) Bessel Functions–Complex Order and Argument

  • Thompson and Barnett (1985). Fortran.

§10.77(ix) Integrals of Bessel Functions

  • Amos (1983a). Fortran.

  • Anderson (1982). Fortran.

  • Lemoine (1997). Fortran.

  • MacLeod (1996a). Fortran.

  • Piessens (1982). Fortran.

  • Sommer and Zabolitzky (1979). Fortran.

  • Talman (1983). Fortran.

  • Weider (1999). Fortran.

See also Chave (1983), Feuillebois (1991), and Piessens and Branders (1984).

§10.77(x) Zeros of Bessel Functions

  • Campbell (1984). Fortran.

  • Kravanja et al. (1998). Fortran.

  • Vrahatis et al. (1995). Fortran.

See also Temme (1979a).