CALGO 715

Algorithm 715.

Procedures:

• caljy0: Bessel functions $J_0(x)$ and $Y_0(x)$
• caljy1: Bessel functions $J_1(x)$ and $Y_1(x)$

Other CALGO 715 procedures not yet included in this module:

• calcei: Exponential integrals $\mathrm{Ei}(x)$ and $\mathrm{E}_1(x)$
• gamma: Gamma function $\Gamma(x)$
• algama: Log Gamma function $\ln\Gamma(x)$
• psi: Digamma function $\psi(x)$
• calerf: Error function $\mathrm{erf}(x)$
• daw: Dawson's integral $e^{-x^2} \int_{0}^{x} e^{t^2} dt$
• anorm: Normal distribution $\frac{1}{\sqrt{2\pi}} \int_{-\infty}^{x} e^{\frac{-t^2}{2}} dt$
• rjbesl: Bessel function $J_{\nu}(x)$
• rybesl: Bessel function $Y_{\nu}(x)$
• calci0: Bessel function $I_0(x)$
• calci1: Bessel function $I_1(x)$
• ribesl: Bessel function $I_{\nu}(x)$
• calck0: Bessel function $K_0(x)$
• calck1: Bessel function $K_1(x)$
• rkbesl: Bessel function $K_{\nu}(x)$

Author

W. J. Cody

History

• 1992-03-15 - W. J. Cody
  • Original code.
• 2000-03-30 - W. J. Cody
  • F77 code distributed by ACM: https://calgo.acm.org/715.zip
• 2003-01-14 - Alan Miller
  • F90 code adaptation by Alan Miller: https://jblevins.org/mirror/amiller/toms715.zip
• 2025-06-17 - Rodrigo Castro (GitHub: rodpcastro)
  • Retained only subroutines caljy0 and caljy1; additional subroutines will be included as required.
  • Replaced dp (double precision) by wp (working precision).
  • Replaced array constructor (/.../) by the less verbose [...].
  • xmax is set such that xmax $> \frac{2}{\pi \epsilon^2}$ , where $\epsilon$ is the machine epsilon.
  • xinf is set to huge(0.0_wp).

References

1. W. J. Cody. 1993. Algorithm 715: SPECFUN–a portable FORTRAN package of special function routines and test drivers. ACM Trans. Math. Softw. 19, 1 (March 1993), 22–30. https://doi.org/10.1145/151271.151273