TSIL_COMPLEX TSIL_Tx0y (TSIL_REAL X, TSIL_REAL Y, TSIL_COMPLEX S,
TSIL_REAL QQ)
{
TSIL_COMPLEX sqDeltaSXY, tp, tm, log1mtp, log1mtm;
TSIL_REAL lnbarX, lnbarY;
if (X < TSIL_TOL) {
TSIL_Warn("TSIL_Tx0y", "T(x,0,y) is undefined for x = 0.");
return TSIL_Infinity;
}
if (TSIL_CABS(S) < TSIL_TOL) return -TSIL_I2p(X, 0.0L, Y, QQ);
if (Y < TSIL_TOL) return TSIL_Tx00(X, S, QQ);
S = TSIL_AddIeps(S);
sqDeltaSXY = TSIL_CSQRT(X*X + Y*Y + S*S - 2.0L*X*Y - 2.0L*X*S - 2.0L*Y*S);
lnbarX = TSIL_LOG(X/QQ);
lnbarY = TSIL_LOG(Y/QQ);
tp = (Y - X + S + sqDeltaSXY)/(2.0L * Y);
tm = (Y - X + S - sqDeltaSXY)/(2.0L * Y);
log1mtp = TSIL_CLOG(1.0L - tp);
log1mtm = TSIL_CLOG(1.0L - tm);
return (-TSIL_Dilog (tp) - TSIL_Dilog (tm) + (1.0L - Y/S)*log1mtp*log1mtm
+ sqDeltaSXY * (log1mtp - log1mtm) / (2.0L * S)
+ lnbarX*lnbarY - 0.5L*(lnbarY + 1.0L)*(lnbarY + 1.0L)
+ (3.0L*S + Y - X) *(lnbarY-lnbarX)/(2.0L * S));
}
TSIL_COMPLEX TSIL_TyyxAtx (TSIL_REAL X, TSIL_REAL Y, TSIL_REAL QQ)
{
TSIL_REAL lnbarX, lnbarY;
if (X < TSIL_TOL) return -TSIL_I2p(Y,Y,0,QQ);
if (Y < TSIL_TOL) {
TSIL_Warn("TSIL_TyyxAtx", "T(y,y,x) with s = 0 is undefined for x = 0.");
return TSIL_Infinity;
}
lnbarX = TSIL_LOG(X/QQ);
lnbarY = TSIL_LOG(Y/QQ);
return -0.5L + (1.0L - Y/X)*(TSIL_Dilog(1.0 -X/Y) -Zeta2)
+ lnbarX - 2.0L*lnbarY + 0.5L*lnbarY*lnbarY;
}
TSIL_COMPLEX TSIL_TxyyAtx (TSIL_REAL X, TSIL_REAL Y, TSIL_REAL QQ)
{
TSIL_REAL lnbarX, lnbarY;
if (X < TSIL_TOL) {
TSIL_Warn("TSIL_TxyyAtx", "T(x,y,y) is undefined for s = x = 0.");
return TSIL_Infinity;
}
if (Y < TSIL_TOL) return TSIL_Tx00(X,X,QQ);
lnbarX = TSIL_LOG(X/QQ);
lnbarY = TSIL_LOG(Y/QQ);
return (-0.5L + (Y/X-1.0L)*(TSIL_Dilog(1.0 -X/Y) -Zeta2)
+ lnbarX*(lnbarY - 1.0L) - 0.5L*lnbarY*lnbarY);
}
TSIL_COMPLEX TSIL_Tx00 (TSIL_REAL X, TSIL_COMPLEX S, TSIL_REAL QQ)
{
TSIL_REAL lnbarX;
if (X < TSIL_TOL) {
TSIL_Warn("TSIL_Tx00", "T(x,0,0) is undefined for x = 0.");
return TSIL_Infinity;
}
if (TSIL_CABS(S) < TSIL_TOL) return -TSIL_I2p(X, 0.0L, 0.0L, QQ);
lnbarX = TSIL_LOG(X/QQ);
if (TSIL_CABS (1.0L - S/X) < 10.0L*TSIL_TOL)
return 2.0L*Zeta2 -0.5L -lnbarX + 0.5L*lnbarX*lnbarX;
S = TSIL_AddIeps(S);
return Zeta2 - 0.5L + (1.0L - X/S)*TSIL_CLOG(1.0L -S/X)
-lnbarX + 0.5L*lnbarX*lnbarX + TSIL_Dilog (S/X);
}
TSIL_COMPLEX TSIL_Beps0x (TSIL_REAL x, TSIL_COMPLEX s, TSIL_REAL qq)
{
TSIL_COMPLEX sqrtx, lnbarx, log1msox, lnbarms;
if (TSIL_CABS(s) < TSIL_TOL) return TSIL_BepsAtZero (0, x, qq);
if (x < TSIL_TOL) {
lnbarms = TSIL_CLOG(-TSIL_AddIeps(s)/qq);
return 4.0L - Zeta2/2.0L - 2.0L*lnbarms + lnbarms*lnbarms/2.0L;
}
sqrtx = TSIL_CSQRT(x);
lnbarx = TSIL_CLOG(x/qq);
if (TSIL_CABS(1 - s/x) < 10.0*TSIL_TOL)
return 4.0L + Zeta2/2.0L + lnbarx*(lnbarx - 4.0L)/2.0L;
log1msox = TSIL_CLOG(1.0L - TSIL_AddIeps(s)/x);
return 4.0L + Zeta2/2.0L - 2.0L*lnbarx + lnbarx*lnbarx/2.0L
+ (1.0L - x/s)*(lnbarx*log1msox - 2.0L*log1msox
+ log1msox*log1msox/2.0L -TSIL_Dilog(s/(s-x)));
}
TSIL_COMPLEX TSIL_Beps (TSIL_REAL X, TSIL_REAL Y, TSIL_COMPLEX S, TSIL_REAL QQ)
{
TSIL_COMPLEX sqrtdeltasxy, t1, t2, t3, t4, logt1, logt2, logt3, logt4;
TSIL_COMPLEX log1mt1, log1mt2, sqrtx, sqrty, lnbarx, lnbary;
TSIL_REAL temp;
if (X < Y) {temp = X; X = Y; Y = temp;}
if (TSIL_CABS(S) < TSIL_TOL) return TSIL_BepsAtZero (X, Y, QQ);
if (Y < TSIL_TOL) return TSIL_Beps0x (X, S, QQ);
sqrtx = TSIL_CSQRT(X);
sqrty = TSIL_CSQRT(Y);
lnbarx = TSIL_CLOG(X/QQ);
lnbary = TSIL_CLOG(Y/QQ);
if (TSIL_CABS(S - (sqrtx + sqrty)*(sqrtx + sqrty))/(X+Y) < 10.0*TSIL_TOL)
return 4.0L + Zeta2/2.0L
+ (sqrtx*lnbarx*(lnbarx - 4.0L) +
sqrty*lnbary*(lnbary - 4.0L))/(2.0L*(sqrtx + sqrty));
if (TSIL_CABS(S - (sqrtx - sqrty)*(sqrtx - sqrty))/(X+Y) < 10.0*TSIL_TOL)
return 4.0L + Zeta2/2.0L
+ (sqrtx*lnbarx*(lnbarx - 4.0L) -
sqrty*lnbary*(lnbary - 4.0L))/(2.0L*(sqrtx - sqrty));
S = TSIL_AddIeps(S);
sqrtdeltasxy = TSIL_CSQRT(TSIL_Delta(S,X,Y));
t1 = ( S - X + Y + sqrtdeltasxy)/(2.0L*sqrtdeltasxy);
t2 = (-S - X + Y + sqrtdeltasxy)/(2.0L*sqrtdeltasxy);
t3 = (-S + X + Y + sqrtdeltasxy)/(2.0L*X);
t4 = (-S + X + Y - sqrtdeltasxy)/(2.0L*X);
/* printf("\ns = ");TSIL_cprintf(S);printf("\n"); */
/* printf("x = %Lf\n", X); */
/* printf("y = %Lf\n", Y); */
/* printf("sqrtdeltasxy = ");TSIL_cprintf(sqrtdeltasxy);printf("\n"); */
/* printf("\nt1 = ");TSIL_cprintf(t1);printf("\n"); */
/* printf("t2 = ");TSIL_cprintf(t2);printf("\n"); */
/* printf("t3 = ");TSIL_cprintf(t3);printf("\n"); */
/* printf("t4 = ");TSIL_cprintf(t4);printf("\n"); */
logt1 = TSIL_CLOG(t1);
logt2 = TSIL_CLOG(t2);
logt3 = TSIL_CLOG(t3);
logt4 = TSIL_CLOG(t4);
/* printf("\nlogt1 = ");TSIL_cprintf(logt1);printf("\n"); */
/* printf("logt2 = ");TSIL_cprintf(logt2);printf("\n"); */
/* printf("logt3 = ");TSIL_cprintf(logt3);printf("\n"); */
/* printf("logt4 = ");TSIL_cprintf(logt4);printf("\n"); */
log1mt1 = TSIL_CLOG(1.0L - t1);
log1mt2 = TSIL_CLOG(1.0L - t2);
return 4.0L + Zeta2/2.0L + (lnbarx*lnbarx + lnbary*lnbary)/4.0L
- lnbarx - lnbary + (sqrtdeltasxy*(TSIL_Dilog(t2) - TSIL_Dilog(t1)
+ (logt3 - logt4)*(1.0L - lnbarx/4.0L - lnbary/4.0L)
+ (log1mt1 + log1mt2)*(logt2 - logt1)/2.0L)
+ (X - Y)*(lnbary - lnbarx)*(1.0L - lnbarx/4.0L - lnbary/4.0L))/S;
}
