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float x5_const[7] = { 2.723987182E+01, 2.433564214E+01, 2.157974547,
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float x5_const[7] = { 2.723987182E+01, 2.433564214E+01, 2.157974547,
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                      4.580044419E-03, 1.047977675E-6 , 4.078415017E-10,
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                      4.580044419E-03, 1.047977675E-6 , 4.078415017E-10,
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                      5.024239358E-11 };
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                      5.024239358E-11 };
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/* Copied from the Project #2 Handout.
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 *
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 * FOR TESTING ONLY
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 */
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float Bessel_Recursive_BU (int n, float x, float base0, float base1)
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{
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    if (n == 0)
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        return base0;
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    else if (n == 1)
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        return base1;
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    return Bessel_Recursive_BU (n-2, x, base0, base1)
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           + 2.0F * (float)(n-1) * Bessel_Recursive_BU (n-1, x, base0, base1) / x;
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}
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float Bessel_Recursive_TD (int n, float x, float base19, float base20)
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{
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    if (n == 19)
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        return base19;
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    else if (n == 20)
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        return base20;
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    return (2.0F * (float)(n+1) / x) * Bessel_Recursive_TD (n+1, x, base19, base20)
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           + Bessel_Recursive_TD (n+2, x, base19, base20);
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}
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/* Find the Bessel Function.
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/* Find the Bessel Function.
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 * Algorithm: I[n+1](x) = I[n-1](x) - (2*n/x) * I[n](x)
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 * Algorithm: I[n+1](x) = I[n-1](x) - (2*n/x) * I[n](x)
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 * Which is equvalent to: I[n](x) = I[n-2](x) - (2 * (n-1)/x) * I[n-1](x)
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 * Which is equvalent to: I[n](x) = I[n-2](x) - (2 * (n-1)/x) * I[n-1](x)
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 * by simple substitution.
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 * by simple substitution.
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 *
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 *
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             << setw(20) << calc_val
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             << setw(20) << calc_val
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             << setw(20) << abs_err
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             << setw(20) << abs_err
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             << setw(20) << rel_err
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             << setw(20) << rel_err
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             << endl;
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             << endl;
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    }
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    }
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    cout << endl;
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}
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}
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int main (void)
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int main (void)
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{
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{
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    print_table (1.0, &Bessel_BottomUp);
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    print_table (1.0, &Bessel_BottomUp);
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    cout << endl;
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    print_table (2.0, &Bessel_BottomUp);
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    print_table (2.0, &Bessel_BottomUp);
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    cout << endl;
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    print_table (5.0, &Bessel_BottomUp);
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    print_table (5.0, &Bessel_BottomUp);
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    cout << endl;
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    cout << endl << endl;
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    print_table (1.0, &Bessel_TopDown);
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    print_table (2.0, &Bessel_TopDown);
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    print_table (5.0, &Bessel_TopDown);
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    return 0;
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    return 0;
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}
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}
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