C341 Modified Bessel Functions K of Certain Order

Subroutine subprograms BSKA and DBSKA calculate the sequence of modified Bessel functions

$K$_a+n(x)

for real argument x>0 and a chosen $a\; \in 0,\hspace{0.17em}\{12\},\hspace{0.17em}\{13\},\hspace{0.17em}\{14\},\hspace{0.17em}\{23\},\hspace{0.17em}\{34\}$ .
On CDC and Cray computers, the double-precision versions DBSKA and DEBKA are not available.

Structure:

SUBROUTINE subprograms
User Entry Names: BSKA, EBSKA, DBSKA,DEBKA
Files Referenced: Unit 6
External References:

BESK0,	BESK1,	EBESK0,	EBESK1,
DBESK0,	DBESK1,	DEBSK0,	DEBSK1	(C313),
BSKR4,	EBSKR4,	DBSKR4,	DEBKR4	(C327),
BSKR3,	EBSKR3,	DBSKR3,	DEBKR3	(C340),
4lMTLMTR(N002), ABEND(Z035)

Usage:

Single-precision version:
CALL BSKA(X,IA,JA,NL,B) or CALL EBSKA(X,IA,JA,NL,B)

X

( REAL) Argument x.

IA,JA

( INTEGER) Numerator i and denominator j of $a=i/j$ . Only the pairs

          (IA,JA) = (0,1), (1,2), (1,3), (1,4), (2,3), (3,4)

are permitted. For example, $IA=2$ and $JA=3$ corresponds to $a=2/3$ .

NL

( INTEGER) Specifies the order $a+NL$ of the last Bessel function in the computed sequence.

B

( REAL) One-dimensional array with dimension ( 0:d) where $d\ge NL$ .
On exit, $B(n)$ , $(n\; =\; 0,1,2,...,NL)$ , contains $K$_a+n(X) for BSKA, $exp(X)*K$_a+n(X) for EBSKA, respectively.

Method:

The well-known recurrence relation for modified Bessel functions is used.

Restrictions:

$X\; >\; 0$ , $NL\; \le 100$ . Only the pairs ( IA,JA) given above are permitted.

Error handling:

Error C341.1: $X\; \le 0$ .
Error C341.2: Pair ( IA,JA) not permitted.
Error C341.3: $NL>100$ .
In all cases, a message is written on Unit 6, unless subroutine MTLSET (N002) has been called. The initial contents of array B is left unchanged.
$•$

C342