CDC 6600 subroutines for Bessel functions J. nu. (x), x greater than or equal to O,. nu. greater than or equal to O and Airy functions Ai(x), Ai'(x), - infinity < x < infinity. [BESJ, AIRY, and DAIRY, in FORTRAN]
Technical Report
·
OSTI ID:7228483
Subroutine BESJ implements the power series, the asymptotic expansion for x ..-->.. infinity, and the uniform asymptotic expansion for ..nu.. ..-->.. infinity for J/sub ..nu../(x). In the region x > ..nu.. forward recursion is stable, and values from the asymptotic expansion for x ..-->.. infinity with small ..nu.. are used to start the recursion for x > 20. Except for x < /sup 1///sub 2/, where the series is used, the Miller backward recursive algorithm, normalized by the power series for the expansion for ..nu.. ..-->.. infinity, is utilized to compute sequences of Bessel functions and cover other parts of the (..nu..,x) plane where no normalization expression is available. The normalization is always computed first with the leading term tested for underflow before any extensive computation is done. Chebyshev expansions on appropriate intervals are used in functions AIRY and DAIRY for the Airy functions Ai(x) and Ai'(x), respectively. A scaling option to remove the exponential decay for x > 0 is also available. 2 figures
- Research Organization:
- Sandia Labs., Albuquerque, NM (USA)
- DOE Contract Number:
- EY-76-C-04-0789
- OSTI ID:
- 7228483
- Report Number(s):
- SAND-75-0147
- Country of Publication:
- United States
- Language:
- English
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