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decuslib20-02
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decus/20-0026/inue.doc
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SUBROUTINE INUE
PURPOSE
COMPUTE THE MODIFIED BESSEL FUNCTIONS I FOR ORDERS 1 TO N
USAGE
CALL INUE(X,N,ZI,RI)
DESCRIPTION OF PARAMETERS
X -GIVEN ARGUMENT OF THE BESSEL FUNCTIONS I
N -GIVEN MAXIMUM ORDER OF BESSEL FUNCTIONS I
ZI -GIVEN VALUE OF BESSEL FUNCTION I OF ORDER ZERO
FOR ARGUMENT X
RI -RESULTANT VECTOR OF DIMENSION N, CONTAINING THE
VALUES OF THE FUNCTIONS I FOR ORDERS 1 TO N
REMARKS
THE VALUE OF ZI MAY BE CALCULATED USING SUBROUTINE I0.
USING A DIFFERENT VALUE HAS THE EFFECT THAT ALL VALUES OF
BESSEL FUNCTIONS I ARE MULTIPLIED BY THE FACTOR ZI/I(0,X)
WHERE I(0,X) IS THE VALUE OF I FOR ORDER 0 AND ARGUMENT X.
THIS MAY BE USED DISADVANTAGEOUSLY IF ONLY THE RATIOS OF I
FOR DIFFERENT ORDERS ARE REQUIRED.
SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
NONE
METHOD
THE VALUES ARE OBTAINED USING BACKWARD RECURRENCE RELATION
TECHNIQUE. THE RATIO I(N+1,X)/I(N,X) IS OBTAINED FROM A
CONTINUED FRACTION.
FOR REFERENCE SEE
G. BLANCH,'NUMERICAL EVALUATION OF CONTINUED FRACTIONS',
SIAM REVIEW, VOL.6,NO.4,1964,PP.383-421.