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```SUBROUTINE ELI2

PURPOSE
COMPUTES THE GENERALIZED ELLIPTIC INTEGRAL OF SECOND KIND

USAGE
CALL ELI2(R,X,CK,A,B)

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

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

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.
```