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diff --git a/src/main/java/org/apache/commons/math3/util/ContinuedFraction.java b/src/main/java/org/apache/commons/math3/util/ContinuedFraction.java
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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math3.util;
+
+import org.apache.commons.math3.exception.ConvergenceException;
+import org.apache.commons.math3.exception.MaxCountExceededException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+
+/**
+ * Provides a generic means to evaluate continued fractions. Subclasses simply provided the a and b
+ * coefficients to evaluate the continued fraction.
+ *
+ * <p>References:
+ *
+ * <ul>
+ *   <li><a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction</a>
+ * </ul>
+ */
+public abstract class ContinuedFraction {
+    /** Maximum allowed numerical error. */
+    private static final double DEFAULT_EPSILON = 10e-9;
+
+    /** Default constructor. */
+    protected ContinuedFraction() {
+        super();
+    }
+
+    /**
+     * Access the n-th a coefficient of the continued fraction. Since a can be a function of the
+     * evaluation point, x, that is passed in as well.
+     *
+     * @param n the coefficient index to retrieve.
+     * @param x the evaluation point.
+     * @return the n-th a coefficient.
+     */
+    protected abstract double getA(int n, double x);
+
+    /**
+     * Access the n-th b coefficient of the continued fraction. Since b can be a function of the
+     * evaluation point, x, that is passed in as well.
+     *
+     * @param n the coefficient index to retrieve.
+     * @param x the evaluation point.
+     * @return the n-th b coefficient.
+     */
+    protected abstract double getB(int n, double x);
+
+    /**
+     * Evaluates the continued fraction at the value x.
+     *
+     * @param x the evaluation point.
+     * @return the value of the continued fraction evaluated at x.
+     * @throws ConvergenceException if the algorithm fails to converge.
+     */
+    public double evaluate(double x) throws ConvergenceException {
+        return evaluate(x, DEFAULT_EPSILON, Integer.MAX_VALUE);
+    }
+
+    /**
+     * Evaluates the continued fraction at the value x.
+     *
+     * @param x the evaluation point.
+     * @param epsilon maximum error allowed.
+     * @return the value of the continued fraction evaluated at x.
+     * @throws ConvergenceException if the algorithm fails to converge.
+     */
+    public double evaluate(double x, double epsilon) throws ConvergenceException {
+        return evaluate(x, epsilon, Integer.MAX_VALUE);
+    }
+
+    /**
+     * Evaluates the continued fraction at the value x.
+     *
+     * @param x the evaluation point.
+     * @param maxIterations maximum number of convergents
+     * @return the value of the continued fraction evaluated at x.
+     * @throws ConvergenceException if the algorithm fails to converge.
+     * @throws MaxCountExceededException if maximal number of iterations is reached
+     */
+    public double evaluate(double x, int maxIterations)
+            throws ConvergenceException, MaxCountExceededException {
+        return evaluate(x, DEFAULT_EPSILON, maxIterations);
+    }
+
+    /**
+     * Evaluates the continued fraction at the value x.
+     *
+     * <p>The implementation of this method is based on the modified Lentz algorithm as described on
+     * page 18 ff. in:
+     *
+     * <ul>
+     *   <li>I. J. Thompson, A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and
+     *       Order." <a target="_blank"
+     *       href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf">
+     *       http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a>
+     * </ul>
+     *
+     * <b>Note:</b> the implementation uses the terms a<sub>i</sub> and b<sub>i</sub> as defined in
+     * <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction @
+     * MathWorld</a>.
+     *
+     * @param x the evaluation point.
+     * @param epsilon maximum error allowed.
+     * @param maxIterations maximum number of convergents
+     * @return the value of the continued fraction evaluated at x.
+     * @throws ConvergenceException if the algorithm fails to converge.
+     * @throws MaxCountExceededException if maximal number of iterations is reached
+     */
+    public double evaluate(double x, double epsilon, int maxIterations)
+            throws ConvergenceException, MaxCountExceededException {
+        final double small = 1e-50;
+        double hPrev = getA(0, x);
+
+        // use the value of small as epsilon criteria for zero checks
+        if (Precision.equals(hPrev, 0.0, small)) {
+            hPrev = small;
+        }
+
+        int n = 1;
+        double dPrev = 0.0;
+        double cPrev = hPrev;
+        double hN = hPrev;
+
+        while (n < maxIterations) {
+            final double a = getA(n, x);
+            final double b = getB(n, x);
+
+            double dN = a + b * dPrev;
+            if (Precision.equals(dN, 0.0, small)) {
+                dN = small;
+            }
+            double cN = a + b / cPrev;
+            if (Precision.equals(cN, 0.0, small)) {
+                cN = small;
+            }
+
+            dN = 1 / dN;
+            final double deltaN = cN * dN;
+            hN = hPrev * deltaN;
+
+            if (Double.isInfinite(hN)) {
+                throw new ConvergenceException(
+                        LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE, x);
+            }
+            if (Double.isNaN(hN)) {
+                throw new ConvergenceException(
+                        LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE, x);
+            }
+
+            if (FastMath.abs(deltaN - 1.0) < epsilon) {
+                break;
+            }
+
+            dPrev = dN;
+            cPrev = cN;
+            hPrev = hN;
+            n++;
+        }
+
+        if (n >= maxIterations) {
+            throw new MaxCountExceededException(
+                    LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION, maxIterations, x);
+        }
+
+        return hN;
+    }
+}