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Annotation of 43BSD/usr.lib/libm/jn.c, revision 1.1

1.1     ! root        1: #ifndef lint
        !             2: static char sccsid[] = "@(#)jn.c       4.2 (Berkeley) 8/21/85";
        !             3: #endif not lint
        !             4: 
        !             5: /*
        !             6:        floating point Bessel's function of
        !             7:        the first and second kinds and of
        !             8:        integer order.
        !             9: 
        !            10:        int n;
        !            11:        double x;
        !            12:        jn(n,x);
        !            13: 
        !            14:        returns the value of Jn(x) for all
        !            15:        integer values of n and all real values
        !            16:        of x.
        !            17: 
        !            18:        There are no error returns.
        !            19:        Calls j0, j1.
        !            20: 
        !            21:        For n=0, j0(x) is called,
        !            22:        for n=1, j1(x) is called,
        !            23:        for n<x, forward recursion us used starting
        !            24:        from values of j0(x) and j1(x).
        !            25:        for n>x, a continued fraction approximation to
        !            26:        j(n,x)/j(n-1,x) is evaluated and then backward
        !            27:        recursion is used starting from a supposed value
        !            28:        for j(n,x). The resulting value of j(0,x) is
        !            29:        compared with the actual value to correct the
        !            30:        supposed value of j(n,x).
        !            31: 
        !            32:        yn(n,x) is similar in all respects, except
        !            33:        that forward recursion is used for all
        !            34:        values of n>1.
        !            35: */
        !            36: 
        !            37: #include <math.h>
        !            38: #ifdef VAX
        !            39: #include <errno.h>
        !            40: #else  /* IEEE double */
        !            41: static double zero = 0.e0;
        !            42: #endif
        !            43: 
        !            44: double
        !            45: jn(n,x) int n; double x;{
        !            46:        int i;
        !            47:        double a, b, temp;
        !            48:        double xsq, t;
        !            49:        double j0(), j1();
        !            50: 
        !            51:        if(n<0){
        !            52:                n = -n;
        !            53:                x = -x;
        !            54:        }
        !            55:        if(n==0) return(j0(x));
        !            56:        if(n==1) return(j1(x));
        !            57:        if(x == 0.) return(0.);
        !            58:        if(n>x) goto recurs;
        !            59: 
        !            60:        a = j0(x);
        !            61:        b = j1(x);
        !            62:        for(i=1;i<n;i++){
        !            63:                temp = b;
        !            64:                b = (2.*i/x)*b - a;
        !            65:                a = temp;
        !            66:        }
        !            67:        return(b);
        !            68: 
        !            69: recurs:
        !            70:        xsq = x*x;
        !            71:        for(t=0,i=n+16;i>n;i--){
        !            72:                t = xsq/(2.*i - t);
        !            73:        }
        !            74:        t = x/(2.*n-t);
        !            75: 
        !            76:        a = t;
        !            77:        b = 1;
        !            78:        for(i=n-1;i>0;i--){
        !            79:                temp = b;
        !            80:                b = (2.*i/x)*b - a;
        !            81:                a = temp;
        !            82:        }
        !            83:        return(t*j0(x)/b);
        !            84: }
        !            85: 
        !            86: double
        !            87: yn(n,x) int n; double x;{
        !            88:        int i;
        !            89:        int sign;
        !            90:        double a, b, temp;
        !            91:        double y0(), y1();
        !            92: 
        !            93:        if (x <= 0) {
        !            94: #ifdef VAX
        !            95:                extern double infnan();
        !            96:                return(infnan(EDOM));   /* NaN */
        !            97: #else  /* IEEE double */
        !            98:                return(zero/zero);      /* IEEE machines: invalid operation */
        !            99: #endif
        !           100:        }
        !           101:        sign = 1;
        !           102:        if(n<0){
        !           103:                n = -n;
        !           104:                if(n%2 == 1) sign = -1;
        !           105:        }
        !           106:        if(n==0) return(y0(x));
        !           107:        if(n==1) return(sign*y1(x));
        !           108: 
        !           109:        a = y0(x);
        !           110:        b = y1(x);
        !           111:        for(i=1;i<n;i++){
        !           112:                temp = b;
        !           113:                b = (2.*i/x)*b - a;
        !           114:                a = temp;
        !           115:        }
        !           116:        return(sign*b);
        !           117: }

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