CDC6600/7600 subroutine for Bessel functions K/sub. nu. /(x), x > 0,. nu. greater than or equal to 0. [BESK and BESKNU]
Technical Report
·
OSTI ID:5539784
Formulae for K/sub ..nu../(x) and K/sub ..nu..+1/(x) are implemented on intervals 0 < x less than or equal to 2, 2 < x < 17, x greater than or equal to 17 and -1/2 less than or equal to ..nu.. < 1/2 to start forward recursion for N member sequences K/sub ..nu..+k-1/(x), k = 1, . . ., N. On 0 < x less than or equal to 2 a recursive form of the power series is used, while the backward recursive Miller algorithm is implemented for the confluent hypergeometric representation on 2 < x < 17. For x greater than or equal to 17, K/sub ..nu..(x) and K/sub ..nu..+1(x) are computed from the asymptotic expansion for x ..-->.. infinity. If the initial order ..nu.. is larger than 35, the sequence is started by computing two members with the uniform asymptotic expansion for ..nu.. ..-->.. infinity. Overflow and underflow tests are made on the leading term of the uniform expansion when appropriate. An option for exponential scaling is also provided.
- Research Organization:
- Sandia Labs., Albuquerque, NM (USA)
- DOE Contract Number:
- EY-76-C-04-0789
- OSTI ID:
- 5539784
- Report Number(s):
- SAND-79-0579
- Country of Publication:
- United States
- Language:
- English
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