C CEL2 10
C ..................................................................CEL2 20
C CEL2 30
C SUBROUTINE CEL2 CEL2 40
C CEL2 50
C PURPOSE CEL2 60
C COMPUTES THE GENERALIZED COMPLETE ELLIPTIC INTEGRAL OF CEL2 70
C SECOND KIND. CEL2 80
C CEL2 90
C USAGE CEL2 100
C CALL CEL2(RES,AK,A,B,IER) CEL2 110
C CEL2 120
C DESCRIPTION OF PARAMETERS CEL2 130
C RES - RESULT VALUE CEL2 140
C AK - MODULUS (INPUT) CEL2 150
C A - CONSTANT TERM IN NUMERATOR CEL2 160
C B - FACTOR OF QUADRATIC TERM IN NUMERATOR CEL2 170
C IER - RESULTANT ERROR CODE WHERE CEL2 180
C IER=0 NO ERROR CEL2 190
C IER=1 AK NOT IN RANGE -1 TO +1 CEL2 200
C CEL2 210
C REMARKS CEL2 220
C FOR ABS(AK) GE 1 THE RESULT IS SET TO 1.7E38 IF B IS CEL2 230
C POSITIVE, TO -1.7E38 IF B IS NEGATIVE. CEL2 240
C SPECIAL CASES ARE CEL2 250
C K(K) OBTAINED WITH A = 1, B = 1 CEL2 260
C E(K) OBTAINED WITH A = 1, B = CK*CK WHERE CK IS CEL2 270
C COMPLEMENTARY MODULUS. CEL2 280
C B(K) OBTAINED WITH A = 1, B = 0 CEL2 290
C D(K) OBTAINED WITH A = 0, B = 1 CEL2 300
C WHERE K, E, B, D DEFINE SPECIAL CASES OF THE GENERALIZED CEL2 310
C COMPLETE ELLIPTIC INTEGRAL OF SECOND KIND IN THE USUAL CEL2 320
C NOTATION, AND THE ARGUMENT K OF THESE FUNCTIONS MEANS CEL2 330
C THE MODULUS. CEL2 340
C CEL2 350
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED CEL2 360
C NONE CEL2 370
C CEL2 380
C METHOD CEL2 390
C DEFINITION CEL2 400
C RES=INTEGRAL((A+B*T*T)/(SQRT((1+T*T)*(1+(CK*T)**2))*(1+T*T))CEL2 410
C SUMMED OVER T FROM 0 TO INFINITY). CEL2 420
C EVALUATION CEL2 430
C LANDENS TRANSFORMATION IS USED FOR CALCULATION. CEL2 440
C REFERENCE CEL2 450
C R.BULIRSCH, 'NUMERICAL CALCULATION OF ELLIPTIC INTEGRALS CEL2 460
C AND ELLIPTIC FUNCTIONS', HANDBOOK SERIES SPECIAL FUNCTIONS, CEL2 470
C NUMERISCHE MATHEMATIK VOL. 7, 1965, PP. 78-90. CEL2 480
C CEL2 490
C ..................................................................CEL2 500
C CEL2 510
SUBROUTINE CEL2(RES,AK,A,B,IER) CEL2 520
IER=0 CEL2 530
ARI=2. CEL2 540
GEO=(0.5-AK)+0.5 CEL2 550
GEO=GEO+GEO*AK CEL2 560
RES=A CEL2 570
A1=A+B CEL2 580
B0=B+B CEL2 590
IF(GEO)1,2,6 CEL2 600
1 IER=1 CEL2 610
2 IF(B)3,8,4 CEL2 620
3 RES=-1.7E38 CEL2 630
RETURN CEL2 640
4 RES=1.7E38 CEL2 650
RETURN CEL2 660
5 GEO=GEO*AARI CEL2 670
6 GEO=SQRT(GEO) CEL2 680
GEO=GEO+GEO CEL2 690
AARI=ARI CEL2 700
ARI=ARI+GEO CEL2 710
B0=B0+RES*GEO CEL2 720
RES=A1 CEL2 730
B0=B0+B0 CEL2 740
A1=B0/ARI+A1 CEL2 750
IF(GEO/AARI-0.9999)5,7,7 CEL2 760
7 RES=A1/ARI CEL2 770
RES=RES+0.5707963E0*RES CEL2 780
8 RETURN CEL2 790
END CEL2 800