This is an automated email from the ASF dual-hosted git repository.
erans pushed a commit to branch master
in repository https://gitbox.apache.org/repos/asf/commons-numbers.git
commit a6c34527ce1b25e4f5867c87c46ece02edeab76c
Author: Gilles Sadowski <gillese...@gmail.com>
AuthorDate: Mon Jul 12 12:54:10 2021 +0200
Use MathJaX in Javadoc.
---
.../org/apache/commons/numbers/gamma/LogBeta.java | 49 ++++++++++------------
1 file changed, 23 insertions(+), 26 deletions(-)
diff --git
a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogBeta.java
b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogBeta.java
index 12e4863..84b8da3 100644
---
a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogBeta.java
+++
b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogBeta.java
@@ -17,13 +17,13 @@
package org.apache.commons.numbers.gamma;
/**
- * Computes \( log_e \Beta(p, q) \).
+ * Computes \( log_e B(p, q) \).
* <p>
* This class is immutable.
* </p>
*/
public final class LogBeta {
- /** The threshold value of 10 where the series expansion of the Δ function
applies. */
+ /** The threshold value of 10 where the series expansion of the \( \Delta
\) function applies. */
private static final double TEN = 10;
/** The threshold value of 2 for algorithm switch. */
private static final double TWO = 2;
@@ -34,24 +34,18 @@ public final class LogBeta {
private static final double HALF_LOG_TWO_PI = 0.9189385332046727;
/**
- * The coefficients of the series expansion of the Δ function. This
function
- * is defined as follows:
- * <pre>
- * Δ(x) = log Γ(x) - (x - 0.5) log a + a - 0.5 log 2π,
- * </pre>
+ * The coefficients of the series expansion of the \( \Delta \) function.
+ * This function is defined as follows:
+ * \[
+ * \Delta(x) = \log \Gamma(x) - (x - \frac{1}{2}) \log a + a -
\frac{1}{2} \log 2\pi,
+ * \]
* <p>
* See equation (23) in Didonato and Morris (1992). The series expansion,
- * which applies for x ≥ 10, reads
+ * which applies for \( x \geq 10 \), reads
* </p>
- * <pre>
- * 14
- * ====
- * 1 \ 2 n
- * Δ(x) = --- > d (10 / x)
- * x / n
- * ====
- * n = 0
- * </pre>
+ * \[
+ * \Delta(x) = \frac{1}{x} \sum_{n = 0}^{14} d_n (\frac{10}{x})^{2 n}
+ * \]
*/
private static final double[] DELTA = {
.833333333333333333333333333333E-01,
@@ -77,12 +71,13 @@ public final class LogBeta {
}
/**
- * Returns the value of Δ(b) - Δ(a + b), with 0 ≤ a ≤ b and b ≥ 10. Based
- * on equations (26), (27) and (28) in Didonato and Morris (1992).
+ * Returns the value of \( \Delta(b) - \Delta(a + b) \),
+ * with \( 0 \leq a \leq b \) and \( b \geq 10 \).
+ * Based on equations (26), (27) and (28) in Didonato and Morris (1992).
*
* @param a First argument.
* @param b Second argument.
- * @return the value of {@code Delta(b) - Delta(a + b)}
+ * @return the value of \( \Delta(b) - \Delta(a + b) \)
* @throws IllegalArgumentException if {@code a < 0} or {@code a > b}
* @throws IllegalArgumentException if {@code b < 10}
*/
@@ -121,13 +116,14 @@ public final class LogBeta {
}
/**
- * Returns the value of Δ(p) + Δ(q) - Δ(p + q), with p, q ≥ 10.
+ * Returns the value of \( \Delta(p) + \Delta(q) - \Delta(p + q) \),
+ * with \( p, q \geq 10 \).
* Based on the <em>NSWC Library of Mathematics Subroutines</em>
implementation,
* {@code DBCORR}.
*
* @param p First argument.
* @param q Second argument.
- * @return the value of {@code Delta(p) + Delta(q) - Delta(p + q)}.
+ * @return the value of \( \Delta(p) + \Delta(q) - \Delta(p + q) \).
* @throws IllegalArgumentException if {@code p < 10} or {@code q < 10}.
*/
private static double sumDeltaMinusDeltaSum(final double p,
@@ -152,13 +148,13 @@ public final class LogBeta {
}
/**
- * Returns the value of {@code log B(p, q)} for {@code 0 ≤ x ≤ 1} and
{@code p, q > 0}.
+ * Returns the value of \( \log B(p, q) \) for \( 0 \leq x \leq 1 \) and
\( p, q > 0 \).
* Based on the <em>NSWC Library of Mathematics Subroutines</em>
implementation,
* {@code DBETLN}.
*
* @param p First argument.
* @param q Second argument.
- * @return the value of {@code log(Beta(p, q))}, {@code NaN} if
+ * @return the value of \( \log B(p, q) \), or {@code NaN} if
* {@code p <= 0} or {@code q <= 0}.
*/
public static double value(double p,
@@ -258,13 +254,14 @@ public final class LogBeta {
}
/**
- * Returns the value of log[Γ(b) / Γ(a + b)] for a ≥ 0 and b ≥ 10.
+ * Returns the value of \( \log ( \Gamma(b) / \Gamma(a + b) ) \)
+ * for \( a \geq 0 \) and \( b \geq 10 \).
* Based on the <em>NSWC Library of Mathematics Subroutines</em>
implementation,
* {@code DLGDIV}.
*
* @param a First argument.
* @param b Second argument.
- * @return the value of {@code log(Gamma(b) / Gamma(a + b))}.
+ * @return the value of \( \log(\Gamma(b) / \Gamma(a + b) \).
* @throws IllegalArgumentException if {@code a < 0} or {@code b < 10}.
*/
private static double logGammaMinusLogGammaSum(double a,
