unit Unit2;

interface
Function BESSI0(X:REAL):REAL;
Function BESSK0(X:Real):Real;

implementation
Function BESSI0(X:REAL):REAL;
CONST
    P1 = 1;             P2 = 3.5156229;
    P3 = 3.0899424;     P4 = 1.2067492;
    P5 = 0.2659732;     P6 = 0.0360768;
    P7 = 0.0045813;
    Q1 = 0.39894228;    Q2 = 0.01328592;
    Q3 = 0.00225319;    Q4 = -0.00157565;
    Q5 = 0.00916281;    Q6 = -0.02057706;
    Q7 = 0.02635537;    Q8 = -0.01647633;
    Q9 = 0.00392377;
VAR
    Y,AAA,BBB,AX:Real;
begin
    If Abs(X) < 3.75 Then
      begin
        Y:=Sqr(X / 3.75);
        AAA:=Y * (P5 + Y * (P6 + Y * P7));
        BESSI0:=P1 + Y * (P2 + Y * (P3 + Y * (P4 + AAA)));
      end
    Else
      begin
        AX:=Abs(X);
        Y:=3.75 / AX;
        AAA:=Exp(AX) / Sqrt(AX);
        BBB:=Q4 + Y * (Q5 + Y * (Q6 + Y * (Q7 + Y * (Q8 + Y * Q9))));
        BESSI0:=AAA * (Q1 + Y * (Q2 + Y * (Q3 + Y * BBB)));
      end;
end;

Function BESSK0(X:Real):Real;
const
    P1 = -0.57721566;    P2 = 0.4227842;
    P3 = 0.23069756;     P4 = 0.0348859;
    P5 = 0.00262698;     P6 = 0.0001075;
    P7 = 0.0000074;
    Q1 = 1.25331414;     Q2 = -0.07832358;
    Q3 = 0.02189568;     Q4 = -0.01062446;
    Q5 = 0.00587872;     Q6 = -0.0025154;
    Q7 = 0.00053208;
var
    Y,AAA,BBB:Real;
begin
    If X <= 2 Then
    begin
        Y:=X * X / 4;
        BBB:=Y * (P5 + Y * (P6 + Y * P7));
        AAA:=P1 + Y * (P2 + Y * (P3 + Y * (P4 + BBB)));
        BESSK0:=(-Ln(X / 2) * BESSI0(X)) + AAA;
    end
    Else
    begin
        Y:=2 / X;
        BBB:=Y * (Q5 + Y * (Q6 + Y * Q7));
        AAA:=Q1 + Y * (Q2 + Y * (Q3 + Y * (Q4 + BBB)));
        BESSK0:=(Exp(-X) / Sqrt(X)) * AAA;
    end;
end;

end.