Features:

Bug Fixes/Re-organization: - Special Function Incomplete Gamma Limit Asymptote - Constructor (1) - Special Function Incomplete Gamma Limit Asymptote - Z Zero (2) - Special Function Incomplete Gamma Limit Asymptote - Z Infinity (3) - Special Function Incomplete Gamma Lower Euler Integral (4, 5, 6) - Special Function Incomplete Gamma Lower Euler Integral - Limit (7, 8) - Special Function Incomplete Gamma Lower Euler Integral - Constructor (9, 10) - Special Function Incomplete Gamma Lower Euler Integral - Evaluate (11, 12, 13) - Special Function Incomplete Gamma Lower Limit Power Integrand (14, 15, 16) - Special Function Incomplete Gamma Lower Limit Power Integrand - s (17, 18) - Special Function Incomplete Gamma Lower Limit Power Integrand - Exponent (19, 20) - Special Function Incomplete Gamma Lower Limit Power Integrand - Constructor (21, 22) - Special Function Incomplete Gamma Lower Limit Power Integrand - Evaluate (23, 24) - Special Function Incomplete Gamma Lower Limit Power Integrand - Anti-derivative (25, 26, 27) - Special Function Incomplete Gamma Lower Limit Power Integrand - Evaluate (28, 29) - Special Function Incomplete Gamma Upper Euler Integral (30, 31, 32) - Special Function Incomplete Gamma Upper Euler Integral - Limit (33, 34) - Special Function Incomplete Gamma Upper Euler Integral - Constructor (35, 36) - Special Function Incomplete Gamma Upper Euler Integral - Evaluate (37, 38, 39) Samples: IdeaDRIP: - Regression for Curreny Returns (Results in Exhibits 2.18-2.20) (40-46) - A Short-List of Risk Factors of a Top-down Asset Allocation Exercise (47-60)
lakshmiDRIP · Feb 27, 2024 · 18145ad · 18145ad
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diff --git a/ReleaseNotes/08_01_2023.txt b/ReleaseNotes/08_01_2023.txt
@@ -0,0 +1,31 @@
+
+Features:
+
+Bug Fixes/Re-organization:
+
+	- Special Function Incomplete Gamma Limit Asymptote - Constructor (1)
+	- Special Function Incomplete Gamma Limit Asymptote - Z Zero (2)
+	- Special Function Incomplete Gamma Limit Asymptote - Z Infinity (3)
+	- Special Function Incomplete Gamma Lower Euler Integral (4, 5, 6)
+	- Special Function Incomplete Gamma Lower Euler Integral - Limit (7, 8)
+	- Special Function Incomplete Gamma Lower Euler Integral - Constructor (9, 10)
+	- Special Function Incomplete Gamma Lower Euler Integral - Evaluate (11, 12, 13)
+	- Special Function Incomplete Gamma Lower Limit Power Integrand (14, 15, 16)
+	- Special Function Incomplete Gamma Lower Limit Power Integrand - s (17, 18)
+	- Special Function Incomplete Gamma Lower Limit Power Integrand - Exponent (19, 20)
+	- Special Function Incomplete Gamma Lower Limit Power Integrand - Constructor (21, 22)
+	- Special Function Incomplete Gamma Lower Limit Power Integrand - Evaluate (23, 24)
+	- Special Function Incomplete Gamma Lower Limit Power Integrand - Anti-derivative (25, 26, 27)
+	- Special Function Incomplete Gamma Lower Limit Power Integrand - Evaluate (28, 29)
+	- Special Function Incomplete Gamma Upper Euler Integral (30, 31, 32)
+	- Special Function Incomplete Gamma Upper Euler Integral - Limit (33, 34)
+	- Special Function Incomplete Gamma Upper Euler Integral - Constructor (35, 36)
+	- Special Function Incomplete Gamma Upper Euler Integral - Evaluate (37, 38, 39)
+
+
+Samples:
+
+IdeaDRIP:
+
+	- Regression for Curreny Returns (Results in Exhibits 2.18-2.20) (40-46)
+	- A Short-List of Risk Factors of a Top-down Asset Allocation Exercise (47-60)
diff --git a/ScheduleSheet.xlsx b/ScheduleSheet.xlsx
diff --git a/src/main/java/org/drip/specialfunction/incompletegamma/LowerEulerIntegral.java b/src/main/java/org/drip/specialfunction/incompletegamma/LowerEulerIntegral.java
@@ -1,11 +1,19 @@
 
 package org.drip.specialfunction.incompletegamma;
 
+import org.drip.function.definition.R1ToR1;
+import org.drip.numerical.common.NumberUtil;
+import org.drip.numerical.differentiation.DerivativeControl;
+import org.drip.numerical.integration.NewtonCotesQuadratureGenerator;
+
 /*
  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  */
 
 /*!
+ * Copyright (C) 2025 Lakshmi Krishnamurthy
+ * Copyright (C) 2024 Lakshmi Krishnamurthy
+ * Copyright (C) 2023 Lakshmi Krishnamurthy
  * Copyright (C) 2022 Lakshmi Krishnamurthy
  * Copyright (C) 2021 Lakshmi Krishnamurthy
  * Copyright (C) 2020 Lakshmi Krishnamurthy
@@ -78,7 +86,7 @@
 
 /**
  * <i>LowerEulerIntegral</i> implements the Euler's Second Kind Integral Version of the Lower Incomplete
- * Gamma Function. The References are:
+ * 	Gamma Function. The References are:
  * 
  * <br><br>
  * 	<ul>
@@ -105,41 +113,53 @@
  * 				https://en.wikipedia.org/wiki/Incomplete_gamma_function
  * 		</li>
  * 	</ul>
+ * 
+ * 	It provides the following functionality:
  *
- *	<br><br>
  *  <ul>
- *		<li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
- *		<li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
- *		<li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Implementation Analysis</a></li>
- *		<li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/gammaincomplete/README.md">Upper/Lower Incomplete Gamma Functions</a></li>
+ * 		<li><i>LowerEulerIntegral</i> Constructor</li>
+ * 		<li>Retrieve the Upper Limit</li>
  *  </ul>
  *
+ *  <br>
+ *  <style>table, td, th {
+ *  	padding: 1px; border: 2px solid #008000; border-radius: 8px; background-color: #dfff00;
+ *		text-align: center; color:  #0000ff;
+ *  }
+ *  </style>
+ *  
+ *  <table style="border:1px solid black;margin-left:auto;margin-right:auto;">
+ *		<tr><td><b>Module </b></td> <td><a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></td></tr>
+ *		<tr><td><b>Library</b></td> <td><a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></td></tr>
+ *		<tr><td><b>Project</b></td> <td><a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Implementation and Analysis</a></td></tr>
+ *		<tr><td><b>Package</b></td> <td><a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/incompletegamma/README.md">Upper/Lower Incomplete Gamma Functions</a></td></tr>
+ *  </table>
+ *
  * @author Lakshmi Krishnamurthy
  */
 
-public class LowerEulerIntegral extends org.drip.function.definition.R1ToR1
+public class LowerEulerIntegral extends R1ToR1
 {
-	private double _limit = java.lang.Double.NaN;
+	private double _limit = Double.NaN;
 
 	/**
-	 * LowerEulerIntegral Constructor
+	 * <i>LowerEulerIntegral</i> Constructor
 	 * 
 	 * @param limit The Upper Limit
-	 * @param dc The Derivative Control
+	 * @param derivativeControl The Derivative Control
 	 * 
-	 * @throws java.lang.Exception Thrown if the Inputs are Invalid
+	 * @throws Exception Thrown if the Inputs are Invalid
 	 */
 
 	public LowerEulerIntegral (
-		final org.drip.numerical.differentiation.DerivativeControl dc,
+		final DerivativeControl derivativeControl,
 		final double limit)
-		throws java.lang.Exception
+		throws Exception
 	{
-		super (dc);
+		super (derivativeControl);
 
-		if (!org.drip.numerical.common.NumberUtil.IsValid (_limit = limit))
-		{
-			throw new java.lang.Exception ("LowerEulerIntegral Constructor => Invalid Inputs");
+		if (!NumberUtil.IsValid (_limit = limit)) {
+			throw new Exception ("LowerEulerIntegral Constructor => Invalid Inputs");
 		}
 	}
 
@@ -156,30 +176,19 @@ public double limit()
 
 	@Override public double evaluate (
 		final double s)
-		throws java.lang.Exception
+		throws Exception
 	{
-		if (!org.drip.numerical.common.NumberUtil.IsValid (s))
-		{
-			throw new java.lang.Exception ("LowerEulerIntegral::evaluate => Invalid Inputs");
+		if (!NumberUtil.IsValid (s)) {
+			throw new Exception ("LowerEulerIntegral::evaluate => Invalid Inputs");
 		}
 
-		return org.drip.numerical.integration.NewtonCotesQuadratureGenerator.Zero_PlusOne (
-			0.,
-			_limit,
-			10000
-		).integrate (
-			new org.drip.function.definition.R1ToR1 (null)
-			{
+		return NewtonCotesQuadratureGenerator.Zero_PlusOne (0., _limit, 10000).integrate (
+			new R1ToR1 (null) {
 				@Override public double evaluate (
 					final double t)
-					throws java.lang.Exception
+					throws Exception
 				{
-					return java.lang.Double.isInfinite (t) ? 0. : (0 == t ? 1. :
-						java.lang.Math.pow (
-							t,
-							s - 1
-						)
-					) * java.lang.Math.exp (-t);
+					return Double.isInfinite (t) ? 0. : (0 == t ? 1. : Math.pow (t, s - 1)) * Math.exp (-t);
 				}
 			}
 		);

diff --git a/src/main/java/org/drip/specialfunction/incompletegamma/LowerLimitPowerIntegrand.java b/src/main/java/org/drip/specialfunction/incompletegamma/LowerLimitPowerIntegrand.java
@@ -1,11 +1,18 @@
 
 package org.drip.specialfunction.incompletegamma;
 
+import org.drip.function.definition.R1ToR1;
+import org.drip.numerical.common.NumberUtil;
+import org.drip.numerical.differentiation.DerivativeControl;
+
 /*
  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  */
 
 /*!
+ * Copyright (C) 2025 Lakshmi Krishnamurthy
+ * Copyright (C) 2024 Lakshmi Krishnamurthy
+ * Copyright (C) 2023 Lakshmi Krishnamurthy
  * Copyright (C) 2022 Lakshmi Krishnamurthy
  * Copyright (C) 2021 Lakshmi Krishnamurthy
  * Copyright (C) 2020 Lakshmi Krishnamurthy
@@ -78,7 +85,7 @@
 
 /**
  * <i>LowerLimitPowerIntegrand</i> contains the Integrand that is the Product of the Limit raised to a Power
- * Exponent and the corresponding Lower Incomplete Gamma, for a given s. The References are:
+ * 	Exponent and the corresponding Lower Incomplete Gamma, for a given s. The References are:
  * 
  * <br><br>
  * 	<ul>
@@ -105,46 +112,60 @@
  * 				https://en.wikipedia.org/wiki/Incomplete_gamma_function
  * 		</li>
  * 	</ul>
+ * 
+ * 	It provides the following functionality:
  *
- *	<br><br>
  *  <ul>
- *		<li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
- *		<li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
- *		<li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Implementation Analysis</a></li>
- *		<li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/gammaincomplete/README.md">Upper/Lower Incomplete Gamma Functions</a></li>
+ * 		<li><i>LowerLimitPowerIntegrand</i> Constructor</li>
+ * 		<li>Retrieve s</li>
+ * 		<li>Retrieve the Limit Power Exponent</li>
  *  </ul>
  *
+ *  <br>
+ *  <style>table, td, th {
+ *  	padding: 1px; border: 2px solid #008000; border-radius: 8px; background-color: #dfff00;
+ *		text-align: center; color:  #0000ff;
+ *  }
+ *  </style>
+ *  
+ *  <table style="border:1px solid black;margin-left:auto;margin-right:auto;">
+ *		<tr><td><b>Module </b></td> <td><a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></td></tr>
+ *		<tr><td><b>Library</b></td> <td><a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></td></tr>
+ *		<tr><td><b>Project</b></td> <td><a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Implementation and Analysis</a></td></tr>
+ *		<tr><td><b>Package</b></td> <td><a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/incompletegamma/README.md">Upper/Lower Incomplete Gamma Functions</a></td></tr>
+ *  </table>
+ *
  * @author Lakshmi Krishnamurthy
  */
 
-public class LowerLimitPowerIntegrand extends org.drip.function.definition.R1ToR1
+public class LowerLimitPowerIntegrand extends R1ToR1
 {
-	private double _s = java.lang.Double.NaN;
-	private double _limitExponent = java.lang.Double.NaN;
+	private double _s = Double.NaN;
+	private double _limitExponent = Double.NaN;
 
 	/**
-	 * LowerLimitPowerIntegrand Constructor
+	 * <i>LowerLimitPowerIntegrand</i> Constructor
 	 * 
-	 * @param dc The Derivative Control
+	 * @param derivativeControl The Derivative Control
 	 * @param s s
 	 * @param limitExponent The Limit Power Exponent
 	 * 
-	 * @throws java.lang.Exception Thrown if the Inputs are Invalid
+	 * @throws Exception Thrown if the Inputs are Invalid
 	 */
 
 	public LowerLimitPowerIntegrand (
-		final org.drip.numerical.differentiation.DerivativeControl dc,
+		final DerivativeControl derivativeControl,
 		final double s,
 		final double limitExponent)
-		throws java.lang.Exception
+		throws Exception
 	{
-		super (dc);
+		super (derivativeControl);
 
-		if (!org.drip.numerical.common.NumberUtil.IsValid (_s = s) ||
-			!org.drip.numerical.common.NumberUtil.IsValid (_limitExponent = limitExponent) ||
-				1. >= _limitExponent)
+		if (!NumberUtil.IsValid (_s = s) ||
+			!NumberUtil.IsValid (_limitExponent = limitExponent) ||
+			1. >= _limitExponent)
 		{
-			throw new java.lang.Exception ("LowerLimitPowerIntegrand Constructor => Invalid Inputs");
+			throw new Exception ("LowerLimitPowerIntegrand Constructor => Invalid Inputs");
 		}
 	}
 
@@ -172,48 +193,31 @@ public double limitExponent()
 
 	@Override public double evaluate (
 		final double z)
-		throws java.lang.Exception
+		throws Exception
 	{
-		if (!org.drip.numerical.common.NumberUtil.IsValid (z))
-		{
-			throw new java.lang.Exception ("LowerLimitPowerIntegrand::evaluate => Invalid Inputs");
+		if (!NumberUtil.IsValid (z)) {
+			throw new Exception ("LowerLimitPowerIntegrand::evaluate => Invalid Inputs");
 		}
 
-		return java.lang.Math.pow (
-			z,
-			_limitExponent - 1.
-		) * new org.drip.specialfunction.incompletegamma.LowerEulerIntegral (
-			null,
-			z
-		).evaluate (_s);
+		return Math.pow (z, _limitExponent - 1.) * new LowerEulerIntegral (null, z).evaluate (_s);
 	}
 
-	@Override public org.drip.function.definition.R1ToR1 antiDerivative()
+	@Override public R1ToR1 antiDerivative()
 	{
-		return new org.drip.function.definition.R1ToR1 (null)
-		{
+		return new R1ToR1 (null) {
 			@Override public double evaluate (
 				final double z)
-				throws java.lang.Exception
+				throws Exception
 			{
-				if (!org.drip.numerical.common.NumberUtil.IsValid (z))
-				{
-					throw new java.lang.Exception
-						("LowerLimitPowerIntegrand::antiDerivative::evaluate => Invalid Inputs");
+				if (!NumberUtil.IsValid (z)) {
+					throw new Exception (
+						"LowerLimitPowerIntegrand::antiDerivative::evaluate => Invalid Inputs"
+					);
 				}
 
 				return (
-					java.lang.Math.pow (
-						z,
-						_limitExponent
-					) * new org.drip.specialfunction.incompletegamma.LowerEulerIntegral (
-						null,
-						z
-					).evaluate (_s) +
-					new org.drip.specialfunction.incompletegamma.UpperEulerIntegral (
-						null,
-						z
-					).evaluate (_s + _limitExponent)
+					Math.pow (z, _limitExponent) * new LowerEulerIntegral (null, z).evaluate (_s) +
+						new UpperEulerIntegral (null, z).evaluate (_s + _limitExponent)
 				) / _limitExponent;
 			}
 		};
@@ -222,9 +226,9 @@ public double limitExponent()
 	@Override public double integrate (
 		final double left,
 		final double right)
-		throws java.lang.Exception
+		throws Exception
 	{
-		org.drip.function.definition.R1ToR1 antiDerivative = antiDerivative();
+		R1ToR1 antiDerivative = antiDerivative();
 
 		return antiDerivative.evaluate (right) - antiDerivative.evaluate (left);
 	}