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.