commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DSCompiler.java [1260:1287]:
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            final double x2    = x * x;
            final double f     = 1.0 / (1 - x2);
            double coeff = JdkMath.sqrt(f);
            function[1] = coeff * p[0];
            for (int n = 2; n <= order; ++n) {

                // update and evaluate polynomial P_n(x)
                double v = 0;
                p[n - 1] = (n - 1) * p[n - 2];
                for (int k = n - 1; k >= 0; k -= 2) {
                    v = v * x2 + p[k];
                    if (k > 2) {
                        p[k - 2] = (k - 1) * p[k - 1] + (2 * n - k) * p[k - 3];
                    } else if (k == 2) {
                        p[0] = p[1];
                    }
                }
                if ((n & 0x1) == 0) {
                    v *= x;
                }

                coeff *= f;
                function[n] = coeff * v;
            }
        }

        // apply function composition
        compose(operand, operandOffset, function, result, resultOffset);
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commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DSCompiler.java [1315:1342]:
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            final double x2    = x * x;
            final double f     = 1.0 / (1 - x2);
            double coeff = JdkMath.sqrt(f);
            function[1] = coeff * p[0];
            for (int n = 2; n <= order; ++n) {

                // update and evaluate polynomial P_n(x)
                double v = 0;
                p[n - 1] = (n - 1) * p[n - 2];
                for (int k = n - 1; k >= 0; k -= 2) {
                    v = v * x2 + p[k];
                    if (k > 2) {
                        p[k - 2] = (k - 1) * p[k - 1] + (2 * n - k) * p[k - 3];
                    } else if (k == 2) {
                        p[0] = p[1];
                    }
                }
                if ((n & 0x1) == 0) {
                    v *= x;
                }

                coeff *= f;
                function[n] = coeff * v;
            }
        }

        // apply function composition
        compose(operand, operandOffset, function, result, resultOffset);
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