//--------------------------------------------------------------
// Legendre polynomials for the L<100
function LegendrePolynomial()
{
	this.Const = new Constants();
	
	this.LMAX = 167;
	this.PL;
	this.dPL
	this.d2PL
	this.PL_1;
	this.arrayPL = [];
	//----------------------------------------------------------
	this.fl3 = [];	
	fl3[0]=1.0;
	var fl=0.0,il;
	for(il=1;il<this.LMAX;il++)
	{
		fl = 1*fl+1.0;
		fl3[il]=1.0/fl;
	}
//----------------------------------------------------------
//  2-aya proizvodnaya ot polinoma Legandra
this.d2LegandreP = function(L,x)
{  
	if(L>this.LMAX-2) return 0.;
	if(L<=1) return 0;
	var l,f1=x,f2=1,ff=0,denom,x2;
	for(l=2;l<=L;l++)
	{
		ff=f1*x;
		ff=2.*ff-f2-(ff-f2)*this.fl3[l];
		if(l!=L) {f2=f1; f1=ff;}// ne delaem v poslednii raz
	}
	// polonom
	this.PL  = ff;
	x2 = x*x;
	denom = x2-1; 
	if(Math.abs(denom) < this.Const.small_add) denom = this.Const.small_add;
	denom = 1/denom;
	// 1-ya proizvodnaya
	this.dPL = denom*(L*x*ff - L*f1);
	// 2-ya proizvodnaya
	denom = L*denom*denom;
	ff = denom*(ff*(x2*(L-1)-1) + f1*x*(3-2*L) + (L-1)*f2);
	this.d2PL = ff;
	return ff;
}
//------------------------------------------------------------------------------
//  Nabor polinomov Legendre dlya l<=L i dannogo znacheniya x=cos(th)
this.LegendrePL0ToArray = function(L,x)
{
	if(L>this.LMAX-2) return false;
	
	this.arrayPL = [];
	this.arrayPL[0]=1; if(L==0) return true;
	this.arrayPL[1]=x; if(L==1) return true;
	var f,l;
	for(l=2;l<=L;l++) 
	{
		f = this.arrayPL[l-1]*x; 
		this.arrayPL[l] = 2.*f-this.arrayPL[l-2]-(f-this.arrayPL[l-2])*this.fl3[l];
	}
	return true;
}
//------------------------------------------------------------------------------
//                      L-th Legendre polinom P_L(x)
//  PL_1 = P_(L-1)(x) - needed for calculation of the P_L derrivative
this.Pl0_cos_th = function(L,x) // x=cos(theta)
{
	if(L>this.LMAX-2) return 0.;
	
	if(L==0) {this.PL_1 = 0; return 1;}
	if(L==1) {this.PL_1 = 1; return x;}

	var l,f1=x,f2=1.,ff=0; 
	for(l=2;l<=L;l++)
	{
		ff=f1*x; 
		ff=2.*ff-f2-(ff-f2)*fl3[l]; 
		f2=f1; f1=ff;
	}
	this.PL_1 = f2;
	return ff;
}
//------------------------------------------------------------------------------
//  P_LM(cos(theta)) - Legendre polinom
this.Plm_cos_th = function(L,M,cth) // x=cos(theta)
{
	var 
		lplus=L+1,
		mplus=M+1,
		lx,m,lt,ltt,
		fl1,fl2,
		p1,p2,p3,z,
		polinom=0,
		llx=true;
	if(L>this.LMAX-2) return 0.0;
	
	z = Math.abs(1 - cth*cth);
	z = 0.5*Math.sqrt(z);
	
	ltt=lplus;
	for(m=1;m<=mplus;m++)
	{
		lx=m-1; p2=1.0; fl1=lx;
		if(!llx)
		for(lt=1;lt<=lx;lt++)
		{
			fl1=fl1+1.0;
			p2=(-p2)*fl1*z;
			polinom=0;
		}
		else llx=false;
		
		polinom=p2;
		p1=0.0; fl2=fl1+1.0; ltt=ltt-1;
		for(lt=1;lt<=ltt;lt++)
		{
			p3=(fl2*cth*p2-fl1*p1)*this.fl3[lt];
			fl1=fl1+1.0; fl2=fl2+2.0;
			polinom=p3; p1=p2; p2=p3;
		}
	}
	if(m%2!=0) return -polinom;
	else       return  polinom;
}
}