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Annotation of 43BSDReno/old/libm/libom/jn.c, revision 1.1

1.1     ! root        1: /*     @(#)jn.c        4.1     12/25/82        */
        !             2: 
        !             3: /*
        !             4:        floating point Bessel's function of
        !             5:        the first and second kinds and of
        !             6:        integer order.
        !             7: 
        !             8:        int n;
        !             9:        double x;
        !            10:        jn(n,x);
        !            11: 
        !            12:        returns the value of Jn(x) for all
        !            13:        integer values of n and all real values
        !            14:        of x.
        !            15: 
        !            16:        There are no error returns.
        !            17:        Calls j0, j1.
        !            18: 
        !            19:        For n=0, j0(x) is called,
        !            20:        for n=1, j1(x) is called,
        !            21:        for n<x, forward recursion us used starting
        !            22:        from values of j0(x) and j1(x).
        !            23:        for n>x, a continued fraction approximation to
        !            24:        j(n,x)/j(n-1,x) is evaluated and then backward
        !            25:        recursion is used starting from a supposed value
        !            26:        for j(n,x). The resulting value of j(0,x) is
        !            27:        compared with the actual value to correct the
        !            28:        supposed value of j(n,x).
        !            29: 
        !            30:        yn(n,x) is similar in all respects, except
        !            31:        that forward recursion is used for all
        !            32:        values of n>1.
        !            33: */
        !            34: 
        !            35: #include <math.h>
        !            36: #include <errno.h>
        !            37: 
        !            38: int    errno;
        !            39: 
        !            40: double
        !            41: jn(n,x) int n; double x;{
        !            42:        int i;
        !            43:        double a, b, temp;
        !            44:        double xsq, t;
        !            45:        double j0(), j1();
        !            46: 
        !            47:        if(n<0){
        !            48:                n = -n;
        !            49:                x = -x;
        !            50:        }
        !            51:        if(n==0) return(j0(x));
        !            52:        if(n==1) return(j1(x));
        !            53:        if(x == 0.) return(0.);
        !            54:        if(n>x) goto recurs;
        !            55: 
        !            56:        a = j0(x);
        !            57:        b = j1(x);
        !            58:        for(i=1;i<n;i++){
        !            59:                temp = b;
        !            60:                b = (2.*i/x)*b - a;
        !            61:                a = temp;
        !            62:        }
        !            63:        return(b);
        !            64: 
        !            65: recurs:
        !            66:        xsq = x*x;
        !            67:        for(t=0,i=n+16;i>n;i--){
        !            68:                t = xsq/(2.*i - t);
        !            69:        }
        !            70:        t = x/(2.*n-t);
        !            71: 
        !            72:        a = t;
        !            73:        b = 1;
        !            74:        for(i=n-1;i>0;i--){
        !            75:                temp = b;
        !            76:                b = (2.*i/x)*b - a;
        !            77:                a = temp;
        !            78:        }
        !            79:        return(t*j0(x)/b);
        !            80: }
        !            81: 
        !            82: double
        !            83: yn(n,x) int n; double x;{
        !            84:        int i;
        !            85:        int sign;
        !            86:        double a, b, temp;
        !            87:        double y0(), y1();
        !            88: 
        !            89:        if (x <= 0) {
        !            90:                errno = EDOM;
        !            91:                return(-HUGE);
        !            92:        }
        !            93:        sign = 1;
        !            94:        if(n<0){
        !            95:                n = -n;
        !            96:                if(n%2 == 1) sign = -1;
        !            97:        }
        !            98:        if(n==0) return(y0(x));
        !            99:        if(n==1) return(sign*y1(x));
        !           100: 
        !           101:        a = y0(x);
        !           102:        b = y1(x);
        !           103:        for(i=1;i<n;i++){
        !           104:                temp = b;
        !           105:                b = (2.*i/x)*b - a;
        !           106:                a = temp;
        !           107:        }
        !           108:        return(sign*b);
        !           109: }

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