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SUBROUTINE CEL1

PURPOSE
   CALCULATE COMPLETE ELLIPTIC INTEGRAL OF FIRST KIND

USAGE
   CALL CEL1(RES,AK,IER)

DESCRIPTION OF PARAMETERS
   RES	 - RESULT VALUE
   AK	 - MODULUS (INPUT)
   IER	 - RESULTANT ERROR CODE WHERE
	   IER=0  NO ERROR
	   IER=1  AK NOT IN RANGE -1 TO +1

REMARKS
   THE RESULT IS SET TO 1.E75 IF ABS(AK) GE 1
   FOR MODULUS AK AND COMPLEMENTARY MODULUS CK,
   EQUATION AK*AK+CK*CK=1.0 IS USED.
   AK MUST BE IN THE RANGE -1 TO +1

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   DEFINITION
   CEL1(AK)=INTEGRAL(1/SQRT((1+T*T)*(1+(CK*T)**2)), SUMMED
   OVER T FROM 0 TO INFINITY).
   EQUIVALENT ARE THE DEFINITIONS
   CEL1(AK)=INTEGRAL(1/(COS(T)SQRT(1+(CK*TAN(T))**2)),SUMMED
   OVER T FROM 0 TO PI/2),
   CEL1(AK)=INTEGRAL(1/SQRT(1-(AK*SIN(T))**2),SUMMED OVER T
   FROM 0 TO PI/2), WHERE K=SQRT(1.-CK*CK).
   EVALUATION
   LANDENS TRANSFORMATION IS USED FOR CALCULATION.
   REFERENCE
   R.BULIRSCH, 'NUMERICAL CALCULATION OF ELLIPTIC INTEGRALS
   AND ELLIPTIC FUNCTIONS', HANDBOOK SERIES SPECIAL FUNCTIONS,
   NUMERISCHE MATHEMATIK VOL. 7, 1965, PP. 78-90.