Enter your search terms Submit search form
	Web pdp-10.trailing-edge.com

SUBROUTINE ELI1

PURPOSE
   COMPUTES THE ELLIPTIC INTEGRAL OF FIRST KIND

USAGE
   CALL ELI1(RES,X,CK)

DESCRIPTION OF PARAMETERS
   RES	 - RESULT VALUE
   X	 - UPPER INTEGRATION BOUND (ARGUMENT OF ELLIPTIC
	   INTEGRAL OF FIRST KIND)
   CK	 - COMPLEMENTARY MODULUS

REMARKS
   MODULUS K = SQRT(1.-CK*CK).

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   DEFINITION
   RES=INTEGRAL(1/SQRT((1+T*T)*(1+(CK*T)**2)), SUMMED
   OVER T FROM 0 TO X).
   EQUIVALENT ARE THE DEFINITIONS
   RES=INTEGRAL(1/(COS(T)*SQRT(1+(CK*TAN(T))**2)), SUMMED
   OVER T FROM 0 TO ATAN(X)),
   RES=INTEGRAL(1/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.