Web pdp-10.trailing-edge.com

Trailing-Edge - PDP-10 Archives - decus_20tap2_198111 - decus/20-0026/cel2.doc
There are 2 other files named cel2.doc in the archive. Click here to see a list.
```SUBROUTINE CEL2

PURPOSE
COMPUTES THE GENERALIZED COMPLETE ELLIPTIC INTEGRAL OF
SECOND KIND.

USAGE
CALL CEL2(RES,AK,A,B,IER)

DESCRIPTION OF PARAMETERS
RES	 - RESULT VALUE
AK	 - MODULUS (INPUT)
A	 - CONSTANT TERM IN NUMERATOR
B	 - FACTOR OF QUADRATIC TERM IN NUMERATOR
IER	 - RESULTANT ERROR CODE WHERE
IER=0  NO ERROR
IER=1  AK NOT IN RANGE -1 TO +1

REMARKS
FOR ABS(AK) GE 1 THE RESULT IS SET TO 1.E75 IF B IS
POSITIVE, TO -1.E75 IF B IS NEGATIVE.
SPECIAL CASES ARE
K(K) OBTAINED WITH A = 1, B = 1
E(K) OBTAINED WITH A = 1, B = CK*CK WHERE CK IS
COMPLEMENTARY MODULUS.
B(K) OBTAINED WITH A = 1, B = 0
D(K) OBTAINED WITH A = 0, B = 1
WHERE K, E, B, D DEFINE SPECIAL CASES OF THE GENERALIZED
COMPLETE ELLIPTIC INTEGRAL OF SECOND KIND IN THE USUAL
NOTATION, AND THE ARGUMENT K OF THESE FUNCTIONS MEANS
THE MODULUS.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
NONE

METHOD
DEFINITION
RES=INTEGRAL((A+B*T*T)/(SQRT((1+T*T)*(1+(CK*T)**2))*(1+T*T))
SUMMED OVER T FROM 0 TO INFINITY).
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.

```