int main(void)
{
double gam1,gam2,gampl,gammi,x,xgam1,xgam2,xgampl,xgammi;
for (;;) {
printf("Enter x:\n");
if (scanf("%lf",&x) == EOF) break;
beschb(x,&xgam1,&xgam2,&xgampl,&xgammi);
printf("%5s\n%17s %16s %17s %15s\n%17s %16s %17s %15s\n",
"x","gam1","gam2","gampl","gammi","xgam1","xgam2","xgampl","xgammi");
gampl=1/exp(gammln((float)(1+x)));
gammi=1/exp(gammln((float)(1-x)));
gam1=(gammi-gampl)/(2*x);
gam2=(gammi+gampl)/2;
printf("%5.2f\n\t%16.6e %16.6e %16.6e %16.6e\n",x,gam1,gam2,gampl,gammi);
printf("\t%16.6e %16.6e %16.6e %16.6e\n",xgam1,xgam2,xgampl,xgammi);
}
return 0;
}
void bessjy(double x, double xnu, double *rj, double *ry, double *rjp, double *ryp)
{
int i, isign, l, nl;
double a, b, br, bi, c, cr, ci, d, del, del1, den, di, dlr, dli, dr, e, f, fact, fact2,
fact3, ff, gam, gam1, gam2, gammi, gampl, h, p, pimu, pimu2, q, r, rjl,
rjl1, rjmu, rjp1, rjpl, rjtemp, ry1, rymu, rymup, rytemp, sum, sum1,
temp, w, x2, xi, xi2, xmu, xmu2;
if (x <= 0.0 || xnu < 0.0)
throw;
nl = (x < XMIN ? (int)(xnu + 0.5) : tmax(0, (int)(xnu - x + 1.5)));
xmu = xnu - nl;
xmu2 = xmu * xmu;
xi = 1.0 / x;
xi2 = 2.0 * xi;
w = xi2 / PI;
isign = 1;
h = xnu * xi;
if (h < FPMIN)
h = FPMIN;
b = xi2 * xnu;
d = 0.0;
c = h;
for (i = 1; i <= MAXIT; i++)
{
b += xi2;
d = b - d;
if (fabs(d) < FPMIN)
d = FPMIN;
c = b - 1.0 / c;
if (fabs(c) < FPMIN)
c = FPMIN;
d = 1.0 / d;
del = c * d;
h = del * h;
if (d < 0.0)
isign = -isign;
if (fabs(del - 1.0) < EPS)
break;
}
if (i > MAXIT)
throw;
rjl = isign * FPMIN;
rjpl = h * rjl;
rjl1 = rjl;
rjp1 = rjpl;
fact = xnu * xi;
for (l = nl; l >= 1; l--)
{
rjtemp = fact * rjl + rjpl;
fact -= xi;
rjpl = fact * rjtemp - rjl;
rjl = rjtemp;
}
if (rjl == 0.0)
rjl = EPS;
f = rjpl / rjl;
if (x < XMIN)
{
x2 = 0.5 * x;
pimu = PI * xmu;
fact = (fabs(pimu) < EPS ? 1.0 : pimu / sin(pimu));
d = -log(x2);
e = xmu * d;
fact2 = (fabs(e) < EPS ? 1.0 : sinh(e) / e);
beschb(xmu, &gam1, &gam2, &gampl, &gammi);
ff = 2.0 / PI * fact * (gam1 * cosh(e) + gam2 * fact2 * d);
e = exp(e);
p = e / (gampl * PI);
q = 1.0 / (e * PI * gammi);
pimu2 = 0.5 * pimu;
fact3 = (fabs(pimu2) < EPS ? 1.0 : sin(pimu2) / pimu2);
r = PI * pimu2 * fact3 * fact3;
c = 1.0;
d = -x2 * x2;
sum = ff + r * q;
sum1 = p;
for (i = 1; i <= MAXIT; i++)
{
ff = (i * ff + p + q) / (i * i - xmu2);
c *= (d / i);
p /= (i - xmu);
q /= (i + xmu);
del = c * (ff + r * q);
sum += del;
del1 = c * p - i * del;
sum1 += del1;
if (fabs(del) < (1.0 + fabs(sum))*EPS)
break;
}
if (i > MAXIT)
throw;
rymu = -sum;
ry1 = -sum1 * xi2;
rymup = xmu * xi * rymu - ry1;
rjmu = w / (rymup - f * rymu);
}
else
{
a = 0.25 - xmu2;
p = -0.5 * xi;
q = 1.0;
br = 2.0 * x;
bi = 2.0;
fact = a * xi / (p * p + q * q);
cr = br + q * fact;
ci = bi + p * fact;
den = br * br + bi * bi;
dr = br / den;
di = -bi / den;
dlr = cr * dr - ci * di;
dli = cr * di + ci * dr;
temp = p * dlr - q * dli;
q = p * dli + q * dlr;
p = temp;
for (i = 2; i <= MAXIT; i++)
{
a += 2 * (i - 1);
bi += 2.0;
dr = a * dr + br;
di = a * di + bi;
if (fabs(dr) + fabs(di) < FPMIN)
dr = FPMIN;
fact = a / (cr * cr + ci * ci);
cr = br + cr * fact;
ci = bi - ci * fact;
if (fabs(cr) + fabs(ci) < FPMIN)
cr = FPMIN;
den = dr * dr + di * di;
dr /= den;
di /= -den;
dlr = cr * dr - ci * di;
dli = cr * di + ci * dr;
temp = p * dlr - q * dli;
q = p * dli + q * dlr;
p = temp;
if (fabs(dlr - 1.0) + fabs(dli) < EPS)
break;
}
if (i > MAXIT)
throw;
gam = (p - f) / q;
rjmu = sqrt(w / ((p - f) * gam + q));
rjmu = NRSIGN(rjmu, rjl);
rymu = rjmu * gam;
rymup = rymu * (p + q / gam);
ry1 = xmu * xi * rymu - rymup;
}
fact = rjmu / rjl;
*rj = rjl1 * fact;
*rjp = rjp1 * fact;
for (i = 1; i <= nl; i++)
{
rytemp = (xmu + i) * xi2 * ry1 - rymu;
rymu = ry1;
ry1 = rytemp;
}
*ry = rymu;
*ryp = xnu * xi * rymu - ry1;
}
void bessik(float x, float xnu, float *ri, float *rk, float *rip, float *rkp)
{
void beschb(double x, double *gam1, double *gam2, double *gampl,
double *gammi);
void nrerror(char error_text[]);
int i,l,nl;
double a,a1,b,c,d,del,del1,delh,dels,e,f,fact,fact2,ff,gam1,gam2,
gammi,gampl,h,p,pimu,q,q1,q2,qnew,ril,ril1,rimu,rip1,ripl,
ritemp,rk1,rkmu,rkmup,rktemp,s,sum,sum1,x2,xi,xi2,xmu,xmu2;
if (x <= 0.0 || xnu < 0.0) nrerror("bad arguments in bessik");
nl=(int)(xnu+0.5);
xmu=xnu-nl;
xmu2=xmu*xmu;
xi=1.0/x;
xi2=2.0*xi;
h=xnu*xi;
if (h < FPMIN) h=FPMIN;
b=xi2*xnu;
d=0.0;
c=h;
for (i=1;i<=MAXIT;i++) {
b += xi2;
d=1.0/(b+d);
c=b+1.0/c;
del=c*d;
h=del*h;
if (fabs(del-1.0) < EPS) break;
}
if (i > MAXIT) nrerror("x too large in bessik; try asymptotic expansion");
ril=FPMIN;
ripl=h*ril;
ril1=ril;
rip1=ripl;
fact=xnu*xi;
for (l=nl;l>=1;l--) {
ritemp=fact*ril+ripl;
fact -= xi;
ripl=fact*ritemp+ril;
ril=ritemp;
}
f=ripl/ril;
if (x < XMIN) {
x2=0.5*x;
pimu=PI*xmu;
fact = (fabs(pimu) < EPS ? 1.0 : pimu/sin(pimu));
d = -log(x2);
e=xmu*d;
fact2 = (fabs(e) < EPS ? 1.0 : sinh(e)/e);
beschb(xmu,&gam1,&gam2,&gampl,&gammi);
ff=fact*(gam1*cosh(e)+gam2*fact2*d);
sum=ff;
e=exp(e);
p=0.5*e/gampl;
q=0.5/(e*gammi);
c=1.0;
d=x2*x2;
sum1=p;
for (i=1;i<=MAXIT;i++) {
ff=(i*ff+p+q)/(i*i-xmu2);
c *= (d/i);
p /= (i-xmu);
q /= (i+xmu);
del=c*ff;
sum += del;
del1=c*(p-i*ff);
sum1 += del1;
if (fabs(del) < fabs(sum)*EPS) break;
}
if (i > MAXIT) nrerror("bessk series failed to converge");
rkmu=sum;
rk1=sum1*xi2;
} else {
b=2.0*(1.0+x);
d=1.0/b;
h=delh=d;
q1=0.0;
q2=1.0;
a1=0.25-xmu2;
q=c=a1;
a = -a1;
s=1.0+q*delh;
for (i=2;i<=MAXIT;i++) {
a -= 2*(i-1);
c = -a*c/i;
qnew=(q1-b*q2)/a;
q1=q2;
q2=qnew;
q += c*qnew;
b += 2.0;
d=1.0/(b+a*d);
delh=(b*d-1.0)*delh;
h += delh;
dels=q*delh;
s += dels;
if (fabs(dels/s) < EPS) break;
}
if (i > MAXIT) nrerror("bessik: failure to converge in cf2");
h=a1*h;
rkmu=sqrt(PI/(2.0*x))*exp(-x)/s;
rk1=rkmu*(xmu+x+0.5-h)*xi;
}
rkmup=xmu*xi*rkmu-rk1;
rimu=xi/(f*rkmu-rkmup);
*ri=(rimu*ril1)/ril;
*rip=(rimu*rip1)/ril;
for (i=1;i<=nl;i++) {
rktemp=(xmu+i)*xi2*rk1+rkmu;
rkmu=rk1;
rk1=rktemp;
}
*rk=rkmu;
*rkp=xnu*xi*rkmu-rk1;
}
