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```SUBROUTINE DCEL1

PURPOSE
CALCULATE COMPLETE ELLIPTIC INTEGRAL OF FIRST KIND

USAGE
CALL DCEL1(RES,AK,IER)

DESCRIPTION OF PARAMETERS
RES	 - RESULT VALUE IN DOUBLE PRECISION
AK	 - MODULUS (INPUT) IN DOUBLE PRECISION
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.D0 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.

```