1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.apache.commons.numbers.gamma;
18
19 /**
20 * Scaled complementary error function.
21 *
22 * <p>\[ \operatorname{erfcx}(z) = \operatorname{erfc}(z)\ e^{z^2} \]
23 *
24 * <p>For large z the value is approximately:
25 *
26 * <p>\[ \operatorname{erfcx}(z) = \frac{1}{z \sqrt{\pi}} \]
27 *
28 * @see Erfc
29 * @since 1.1
30 */
31 public final class Erfcx {
32 /** Private constructor. */
33 private Erfcx() {
34 // intentionally empty.
35 }
36
37 /**
38 * Returns the scaled complementary error function.
39 *
40 * <p>Special cases:
41 * <ul>
42 * <li>If the argument is 0, then the result is 1.
43 * <li>If the argument is +infinity, then the result is 0.
44 * <li>If the argument is negative and {@code exp(x*x)} is infinite, then the result is +infinity.
45 * <li>If the argument is nan, then the result is nan.
46 * </ul>
47 *
48 * @param x Value.
49 * @return the scaled complementary error function.
50 */
51 public static double value(double x) {
52 return BoostErf.erfcx(x);
53 }
54 }