PDP-10 Archive: decus/20-0026/djelf.doc from decuslib20-02

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SUBROUTINE DJELF

PURPOSE
   COMPUTES THE THREE JACOBIAN ELLIPTIC FUNCTIONS SN, CN, DN.

USAGE
   CALL DJELF(SN,CN,DN,X,SCK)

DESCRIPTION OF PARAMETERS
   SN	 - RESULT VALUE SN(X) IN DOUBLE PRECISION
   CN	 - RESULT VALUE CN(X) IN DOUBLE PRECISION
   DN	 - RESULT VALUE DN(X) IN DOUBLE PRECISION
   X	 - DOUBLE PRECISION ARGUMENT OF JACOBIAN ELLIPTIC
	   FUNCTIONS
   SCK	 - SQUARE OF COMPLEMENTARY MODULUS IN DOUBLE PRECISION

REMARKS
   NONE

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   DEFINITION
   X=INTEGRAL(1/SQRT((1-T*T)*(1-(K*T)**2)), SUMMED OVER
   T FROM 0 TO SN), WHERE K=SQRT(1-SCK).
   SN*SN + CN*CN = 1
   (K*SN)**2 + DN**2 = 1.
   EVALUATION
   CALCULATION IS DONE USING THE PROCESS OF THE ARITHMETIC
   GEOMETRIC MEAN TOGETHER WITH GAUSS DESCENDING TRANSFORMATION
   BEFORE INVERSION OF THE INTEGRAL TAKES PLACE.
   REFERENCE
   R. BULIRSCH, NUMERICAL CALCULATION OF ELLIPTIC INTEGRALS AND
	  ELLIPTIC FUNCTIOMS.
	  HANDBOOK SERIES OF SPECIAL FUNCTIONS
	  NUMERISCHE MATHEMATIK VOL. 7, 1965, PP. 78-90.