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| <HTML>
<HEAD>
<TITLE>Bessel Function Evaluator in JavaScript</TITLE>
</HEAD>
<BODY bgcolor=#FFFFFF>
<CENTER>
<FORM name="form">
<TABLE border=4>
<TR>
<TD COLSPAN=6 ALIGN=CENTER VALIGN=MIDDLE><H2>Bessel Function Calculator</H2></TD>
</TR>
<TR>
<TD COLSPAN=4 ALIGN=CENTER>
<INPUT TYPE="button" VALUE="Calculate"
onclick=calculate(this.form.x1.value,this.form.x2.value,this.form.x3.value,this.form.n1.value,this.form.n2.value,this.form.n3.value)>
<INPUT TYPE="reset" VALUE="Clear all fields">
</TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>x</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=x1 SIZE=15 onfocus=document.form.x1.select();clear1()></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=x2 SIZE=15 onfocus=document.form.x2.select();clear2()></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=x3 SIZE=15 onfocus=document.form.x3.select();clear3()></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>n</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=n1 SIZE=15 onfocus=document.form.n1.select();clear1()></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=n2 SIZE=15 onfocus=document.form.n2.select();clear2()></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=n3 SIZE=15 onfocus=document.form.n3.select();clear3()></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>J<SUB>0</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=J01 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=J02 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=J03 SIZE=15></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>J<SUB>1</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=J11 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=J12 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=J13 SIZE=15></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>Y<SUB>0</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Y01 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Y02 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Y03 SIZE=15></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>Y<SUB>1</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Y11 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Y12 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Y13 SIZE=15></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>I<SUB>0</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=I01 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=I02 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=I03 SIZE=15></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>I<SUB>1</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=I11 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=I12 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=I13 SIZE=15></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>K<SUB>0</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=K01 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=K02 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=K03 SIZE=15></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>K<SUB>1</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=K11 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=K12 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=K13 SIZE=15></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>J<SUB>n</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Jn1 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Jn2 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Jn3 SIZE=15></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>Y<SUB>n</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Yn1 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Yn2 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Yn3 SIZE=15></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>I<SUB>n</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=In1 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=In2 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=In3 SIZE=15></TD>
</TR>
<TR>
<TD ALIGN=CENTER><I>K<SUB>n</SUB>(x)</I></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Kn1 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Kn2 SIZE=15></TD>
<TD ALIGN=RIGHT><INPUT TYPE=TEXT NAME=Kn3 SIZE=15></TD>
</TR>
<TR>
<TD COLSPAN=4 ALIGN=CENTER>
<INPUT TYPE="button" VALUE="Calculate"
onclick=calculate(this.form.x1.value,this.form.x2.value,this.form.x3.value,this.form.n1.value,this.form.n2.value,this.form.n3.value)>
<INPUT TYPE="reset" VALUE="Clear all fields">
</TD>
</TR>
</TABLE>
</FORM><HR>
</CENTER>
<SCRIPT LANGUAGE="JavaScript">
<!-- Bessel function calculator
function BesselJ0(x) {
var ax,z,xx,y,ans,ans1,ans2;
ax = Math.abs(x)
if (ax < 8.0) {
y = x * x;
ans1 = 57568490574.0 + y * (-13362590354.0 + y * (651619640.7 + y * (-11214424.18 + y * (77392.33017 + y * (-184.9052456)))));
ans2 = 57568490411.0 + y * (1029532985.0 + y * (9494680.718 + y * (59272.64853 + y * (267.8532712 + y * 1.0))));
ans = ans1 / ans2;
} else {
z = 8.0 / ax;
y = z * z;
xx = ax - 0.785398164;
ans1 = 1.0 + y * (-0.1098628627e-2 + y * (0.2734510407e-4 + y * (-0.2073370639e-5 + y * 0.2093887211e-6)));
ans2 = -0.1562499995e-1 + y * (0.1430488765e-3 + y * (-0.6911147651e-5 + y * (0.7621095161e-6 - y * 0.934935152e-7)));
ans = Math.sqrt(0.636619772 / ax) * (Math.cos(xx) * ans1 - z * Math.sin(xx) * ans2);
}
return ans;
}
function BesselJ1(x) {
var ax,z,xx,y,ans,ans1,ans2;
ax = Math.abs(x);
if (ax < 8.0) {
y=x*x;
ans1 = x*(72362614232.0+y*(-7895059235.0+y*(242396853.1+y*(-2972611.439+y*(15704.48260+y*(-30.16036606))))));
ans2 = 144725228442.0+y*(2300535178.0+y*(18583304.74+y*(99447.43394+y*(376.9991397+y*1.0))));
ans = ans1/ans2;
} else {
z=8.0/ax;
y=z*z;
xx=ax-2.356194491;
ans1=1.0+y*(0.183105e-2+y*(-0.3516396496e-4+y*(0.2457520174e-5+y*(-0.240337019e-6))));
ans2=0.04687499995+y*(-0.2002690873e-3+y*(0.8449199096e-5+y*(-0.88228987e-6+y*0.105787412e-6)));
ans=Math.sqrt(0.636619772/ax)*(Math.cos(xx)*ans1-z*Math.sin(xx)*ans2);
if (x < 0.0) ans = -ans;
}
return ans;
}
function BesselY0(x) {
var z, xx, y, ans, ans1, ans2;
if (x < 8.0) {
y=x*x;
ans1 = -2957821389.0+y*(7062834065.0+y*(-512359803.6+y*(10879881.29+y*(-86327.92757+y*228.4622733))));
ans2 = 40076544269.0+y*(745249964.8+y*(7189466.438+y*(47447.26470+y*(226.1030244+y*1.0))));
ans = (ans1/ans2)+0.636619772*BesselJ0(x)*Math.log(x);
} else {
z=8.0/x;
y=z*z;
xx=x-0.785398164;
ans1 = 1.0+y*(-0.1098628627e-2+y*(0.2734510407e-4+y*(-0.2073370639e-5+y*0.2093887211e-6)));
ans2 = -0.1562499995e-1+y*(0.1430488765e-3+y*(-0.6911147651e-5+y*(0.7621095161e-6+y*(-0.934945152e-7))));
ans = Math.sqrt(0.636619772/x)*(Math.sin(xx)+ans1+z*Math.cos(xx)*ans2);
}
return ans;
}
function BesselY1(x) {
var z, xx, y, ans, ans1, ans2;
if (x < 8.0) {
y=x*x
ans1 = x*(-0.4900604943e13+y*(0.1275274390e13+y*(-0.5153438139e11+y*(0.7349264551e9+y*(-0.4237922726e7+y*0.8511937935e4)))));
ans2 = 0.2499580570e14+y*(0.4244419664e12+y*(0.3733650367e10+y*(0.2245904002e8+y*(0.1020426050e6+y*(0.3549632885e3+y)))));
ans = (ans1/ans2)+0.636619772*(BesselJ1(x)*Math.log(x)-1.0/x);
} else {
z=8.0/x;
y=z*z;
xx=x-2.356194491;
ans1=1.0+y*(0.183105e-2+y*(-0.3516396496e-4+y*(0.2457520174e-5+y*(-0.240337019e-6))));
ans2=0.04687499995+y*(-0.202690873e-3+y*(0.8449199096e-5+y*(-0.88228987e-6+y*0.10578e-6)));
ans=Math.sqrt(0.636619772/x)*(Math.sin(xx)*ans1+z*Math.cos(xx)*ans2);
}
return ans;
}
function BesselI0(x) {
var ax,ans,y;
ax=Math.abs(x);
if (ax < 3.75) {
y=x/3.75;
y*=y;
ans=1.0+y*(3.5156229+y*(3.0899424+y*(1.2067492+y*(0.2659732+y*(0.360768e-1+y*0.45813e-2)))));
} else {
y=3.75/ax;
ans=(Math.exp(ax)/Math.sqrt(ax))*(0.39894228+y*(0.1328592e-1+y*(0.225319e-2+y*(-0.157565e-2+y*(0.916281e-2+y*(-0.2057706e-1+y*(0.2635537e-1+y*(-0.1647633e-1+y*0.392377e-2))))))));
}
return ans;
}
function BesselI1(x) {
var ax,ans,y;
ax=Math.abs(x);
if (ax<3.75) {
y=x/3.75;
y*=y;
ans=ax*(0.5+y*(0.87890594+y*(0.51498869+y*(0.15084934+y*(0.2658733e-1+y*(0.301532e-2+y*0.32411e-3))))));
} else {
y=3.75/ax;
ans=0.2282967e-1+y*(-0.2895312e-1+y*(0.1787654e-1-y*0.420059e-2));
ans=0.39894228+y*(-0.3988024e-1+y*(-0.362018e-2+y*(0.163801e-2+y*(-0.1031555e-1+y*ans))));
ans*=(Math.exp(ax)/Math.sqrt(ax));
}
return x < 0.0 ? -ans : ans;
}
function BesselK0(x) {
var y,ans;
if (x <= 2.0) {
y=x*x/4.0;
ans=(-Math.log(x/2.0)*BesselI0(x))-0.57721566+0.42278420*y+0.23069756*y*y+0.03488590*y*y*y+0.00262698*y*y*y*y+0.00010750*y*y*y*y*y+0.00000740*y*y*y*y*y*y;
} else {
y=2.0/x;
ans=(Math.exp(-x)/Math.sqrt(x))*(1.25331414+y*(-0.7832358e-1+y*(0.2189568e-1+y*(-0.1062446e-1+y*(0.587872e-2+y*(-0.251540e-2+y*0.53208e-3))))));
}
return ans;
}
function BesselK1(x) {
var y,ans;
if (x <= 2.0) {
y=x*x/4.0;
ans=(Math.log(x/2.0)*BesselI1(x))+(1.0/x)*(1.0+y*(0.15443144+y*(-0.67278579+y*(-0.18156897+y*(-0.1919402e-1+y*(-0.110404e-2+y*(-0.4686e-4)))))));
} else {
y=2.0/x
ans=(Math.exp(-x)/Math.sqrt(x))*(1.25331414+y*(0.23498619+y*(-0.3655620e-1+y*(0.1504268e-1+y*(-0.780353e-2+y*(0.325614e-2+y*(-0.68245e-3)))))));
}
return ans;
}
function BesselJ(n,x) {
if (n == null || n.length == 0) return "n not specified";
if (Math.floor(n) != n) return "Error: n not integer";
if (n < 2) return "Error: n < 2";
var ACC = 40.0; // Make larger to increase accuracy.
var BIGNO = 1.0e10;
var BIGNI = 1.0e-10;
var j,jsum,m,ax,bj,bjm,bjp,sum,tox,ans;
ax=Math.abs(x);
if (ax == 0.0) return 0.0;
else if (ax > n) {
tox = 2.0/ax;
bjm=BesselJ0(ax);
bj=BesselJ1(ax);
for (j=1;j<n;j++) {
bjp=j*tox*bj-bjm;
bjm=bj;
bj=bjp;
}
ans=bj;
} else {
tox=2.0/ax;
if (Math.sqrt(ACC*n) >= 0)
m=2*((n + Math.floor(Math.sqrt(ACC*n))) / 2);
else
m=2*((n + Math.ceil(Math.sqrt(ACC*n))) / 2);
jsum=0;
bjp=ans=sum=0.0;
bj=1.0;
for (j=m;j>0;j--) {
bjm=j*tox*bj-bjp;
bjp=bj;
bj=bjm;
if (Math.abs(bj) > BIGNO) {
bj *= BIGNI;
bjp *= BIGNI;
ans *= BIGNI;
sum *= BIGNI;
}
if (jsum) sum += bj;
jsum=!jsum;
if (j == n) ans=bjp;
}
sum=2.0*sum-bj;
ans /= sum;
}
return x < 0.0 && (n & 1) ? -ans : ans;
}
function BesselY(n,x) {
if (n == null || n.length == 0) return "n not specified";
if (Math.floor(n) != n) return "Error: n not integer";
if (n < 2) return "Error: n < 2";
var j,by,bym,byp,tox;
tox=2.0/x;
by=BesselY1(x);
bym=BesselY0(x);
for (j=1;j<n;j++) {
byp=j*tox*by-bym;
bym=by;
by=byp;
}
return by;
}
function BesselI(n,x) {
if (n == null || n.length == 0) return "n not specified";
if (Math.floor(n) != n) return "Error: n not integer";
if (n < 2) return "Error: n < 2";
var ACC = 40.0; // Make larger to increase accuracy.
var BIGNO = 1.0e10;
var BIGNI = 1.0e-10;
var j,bi,bim,bip,tox,ans;
if (x == 0.0) return 0.0;
else {
tox=2.0/Math.abs(x);
bip=ans=0.0;
bi=1.0;
for (j=2*(n+Math.floor(Math.sqrt(ACC*n)));j>0;j--) {
bim=bip+j*tox*bi;
bip=bi;
bi=bim;
if (Math.abs(bi) > BIGNO) {
ans *= BIGNI;
bi *= BIGNI;
bip *= BIGNI;
}
if (j == n) ans=bip;
}
ans *= BesselI0(x) / bi;
return x < 0.0 && (n & 1) ? -ans : ans;
}
}
function BesselK(n,x) {
if (n == null || n.length == 0) return "n not specified";
if (Math.floor(n) != n) return "Error: n not integer";
if (n < 2) return "Error: n < 2";
var j,bk,bkm,bkp,tox;
tox=2.0/x;
bkm=BesselK0(x);
bk=BesselK1(x);
for (j=1;j<n;j++) {
bkp=bkm+j*tox*bk;
bkm=bk;
bk=bkp;
0}
return bk;
}
function calculate(x1,x2,x3,n1,n2,n3){
if (x1 != null && x1.length != 0) {
document.form.J01.value = formatnumber(BesselJ0(x1));
document.form.J11.value = formatnumber(BesselJ1(x1));
document.form.Y01.value = formatnumber(BesselY0(x1));
document.form.Y11.value = formatnumber(BesselY1(x1));
document.form.I01.value = formatnumber(BesselI0(x1));
document.form.I11.value = formatnumber(BesselI1(x1));
document.form.K01.value = formatnumber(BesselK0(x1));
document.form.K11.value = formatnumber(BesselK1(x1));
document.form.Jn1.value = formatnumber(BesselJ(n1,x1));
document.form.Yn1.value = formatnumber(BesselY(n1,x1));
document.form.In1.value = formatnumber(BesselI(n1,x1));
document.form.Kn1.value = formatnumber(BesselK(n1,x1));
}
if (x2 != null && x2.length != 0) {
document.form.J02.value = formatnumber(BesselJ0(x2));
document.form.J12.value = formatnumber(BesselJ1(x2));
document.form.Y02.value = formatnumber(BesselY0(x2));
document.form.Y12.value = formatnumber(BesselY1(x2));
document.form.I02.value = formatnumber(BesselI0(x2));
document.form.I12.value = formatnumber(BesselI1(x2));
document.form.K02.value = formatnumber(BesselK0(x2));
document.form.K12.value = formatnumber(BesselK1(x2));
document.form.Jn2.value = formatnumber(BesselJ(n2,x2));
document.form.Yn2.value = formatnumber(BesselY(n2,x2));
document.form.In2.value = formatnumber(BesselI(n2,x2))
document.form.Kn2.value = formatnumber(BesselK(n2,x2));
}
if (x3 != null && x3.length != 0) {
document.form.J03.value = formatnumber(BesselY0(x3));
document.form.J13.value = formatnumber(BesselJ1(x3));
document.form.Y03.value = formatnumber(BesselY0(x3));
document.form.Y13.value = formatnumber(BesselY1(x3));
document.form.I03.value = formatnumber(BesselI0(x3));
document.form.I13.value = formatnumber(BesselI1(x3));
document.form.K03.value = formatnumber(BesselK0(x3));
document.form.K13.value = formatnumber(BesselK1(x3));
document.form.Jn3.value = formatnumber(BesselJ(n3,x3));
document.form.Yn3.value = formatnumber(BesselY(n3,x3));
document.form.In3.value = formatnumber(BesselI(n3,x3));
document.form.Kn3.value = formatnumber(BesselK(n3,x3));
}
}
function formatnumber(number) {
temp = parseFloat(number);
if (isNaN(temp)) {
if (number == "n not specified")
return number;
else if (number == "Error: n not integer")
return number;
else if (number == "Error: n < 2")
return number;
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</HTML> |
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