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```SUBROUTINE DELI2

PURPOSE
COMPUTES THE GENERALIZED ELLIPTIC INTEGRAL OF SECOND KIND

USAGE
CALL DELI2(R,X,CK,A,B)

DESCRIPTION OF PARAMETERS
R	 - RESULT VALUE IN DOUBLE PRECISION
X	 - UPPER INTEGRATION BOUND (ARGUMENT OF ELLIPTIC
INTEGRAL OF SECOND KIND) IN DOUBLE PRECISION
CK	 - COMPLEMENTARY MODULUS IN DOUBLE PRECISION
A	 - DOUBLE PRECISION CONSTANT TERM IN NUMERATOR
B	 - DOUBLE PRECISION QUATRATIC TERM IN NUMERATOR

REMARKS
DOUBLE PRECISION MODULUS K = DSQRT(1.D0-CK*CK).
SPECIAL CASES OF THE GENERALIZED ELLIPTIC INTEGRAL OF
SECOND KIND ARE
F(DATAN(X),K) OBTAINED WITH A=1.D0, B=1.D0
E(DATAN(X),K) OBTAINED WITH A=1.D0, B=CK*CK
B(DATAN(X),K) OBTAINED WITH A=1.D0, B=0.D0
D(DATAN(X),K) OBTAINED WITH A=0.D0, B=1.D0.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
NONE

METHOD
DEFINITION
R=INTEGRAL((A+B*T*T)/(SQRT((1+T*T)*(1+(CK*T)**2))*(1+T*T)),
SUMMED OVER T FROM 0 TO X).
EQUIVALENT IS THE DEFINITION
R=INTEGRAL((A+(B-A)*(SIN(T))**2)/SQRT(1-(K*SIN(T))**2),
SUMMED OVER T FROM 0 TO ATAN(X)).
EVALUATION
LANDENS TRANSFORMATION IS USED FOR CALCULATION.
REFERENCE
R. BULIRSCH, NUMERICAL CALCULATION OF ELLIPTIC INTEGRALS AND
ELLIPTIC FUNCTIONS
HANDBOOK SERIES OF SPECIAL FUNCTIONS
NUMERISCHE MATHEMATIK VOL. 7, 1965, PP. 78-90.

```