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Trailing-Edge - PDP-10 Archives - decuslib20-02 - 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.