Features:

Bug Fixes/Re-organization: - Special Function Definition Hyper-geometric Estimator - Parameters (1) - Special Function Definition Hyper-geometric Estimator - Constructor (2, 3) - Special Function Definition Confluent Hypergeometric Estimator - Constructor (4) - Special Function Definition Confluent Hypergeometric Estimator - Evaluate (5) - Special Function Definition Confluent Hypergeometric Estimator (6) - Special Function Definition Elliptic E Integral Estimator #1 (7, 8) - Special Function Definition Elliptic E Integral Estimator - Constructor (9) - Special Function Definition Elliptic E Integral Estimator #2 (10) - Special Function Definition Elliptic K Integral Estimator #1 (11, 12) - Special Function Definition Elliptic K Integral Estimator - Constructor (13) - Special Function Definition Elliptic K Integral Estimator #2 (14) - Special Function Definition Elliptic E Integral Estimator - Evaluate (15) - Special Function Definition Elliptic K Integral Estimator - Evaluate (16) - Special Function Definition Hankel First Kind Estimator (17, 18, 19) - Special Function Definition Hankel First Kind Estimator - Big H1 (20) - Special Function Definition Hankel First Kind Estimator - Evaluate (21) - Special Function Definition Hankel First Kind Estimator - Large Z Asymptote (22, 23) - Special Function Definition Hankel Second Kind Estimator (24, 25, 26) - Special Function Definition Hankel Second Kind Estimator - Big H2 (27) - Special Function Definition Hankel Second Kind Estimator - Evaluate (28) - Special Function Definition Hankel Second Kind Estimator - Large Z Asymptote (29, 30) - Special Function Definition Jacobi Estimator #1 (31, 32, 33) - Special Function Definition Jacobi Estimator - n (34, 35) - Special Function Definition Jacobi Estimator - Constructor (36, 37) - Special Function Definition Jacobi Estimator - Alpha (38) - Special Function Definition Jacobi Estimator - Beta (39) - Special Function Definition Jacobi Estimator #2 (40) - Special Function Definition Legendre Estimator (41, 42, 43) - Special Function Definition Legendre Estimator - Constructor (44, 45) - Special Function Definition Jacobi Estimator - Alpha (46) - Special Function Definition Jacobi Estimator - Ceta (47) - Special Function Definition Jacobi Estimator - Evaluate (48, 49) - Special Function Definition Modified Bessel First Kind Estimator (50, 51, 52) - Special Function Definition Modified Bessel First Kind Estimator - Alpha Positive Asymptote (53, 54, 55) - Special Function Definition Modified Bessel First Kind Estimator - Big I (56) - Special Function Definition Modified Bessel First Kind Estimator - Evaluate (57) - Special Function Definition Modified Bessel Second Kind Estimator (58, 59, 60) Samples: IdeaDRIP:
lakshmiDRIP · Feb 3, 2024 · 81ed333 · 81ed333
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diff --git a/ReleaseNotes/06_08_2023.txt b/ReleaseNotes/06_08_2023.txt
@@ -0,0 +1,47 @@
+
+Features:
+
+Bug Fixes/Re-organization:
+
+	- Special Function Definition Hyper-geometric Estimator - Parameters (1)
+	- Special Function Definition Hyper-geometric Estimator - Constructor (2, 3)
+	- Special Function Definition Confluent Hypergeometric Estimator - Constructor (4)
+	- Special Function Definition Confluent Hypergeometric Estimator - Evaluate (5)
+	- Special Function Definition Confluent Hypergeometric Estimator (6)
+	- Special Function Definition Elliptic E Integral Estimator #1 (7, 8)
+	- Special Function Definition Elliptic E Integral Estimator - Constructor (9)
+	- Special Function Definition Elliptic E Integral Estimator #2 (10)
+	- Special Function Definition Elliptic K Integral Estimator #1 (11, 12)
+	- Special Function Definition Elliptic K Integral Estimator - Constructor (13)
+	- Special Function Definition Elliptic K Integral Estimator #2 (14)
+	- Special Function Definition Elliptic E Integral Estimator - Evaluate (15)
+	- Special Function Definition Elliptic K Integral Estimator - Evaluate (16)
+	- Special Function Definition Hankel First Kind Estimator (17, 18, 19)
+	- Special Function Definition Hankel First Kind Estimator - Big H1 (20)
+	- Special Function Definition Hankel First Kind Estimator - Evaluate (21)
+	- Special Function Definition Hankel First Kind Estimator - Large Z Asymptote (22, 23)
+	- Special Function Definition Hankel Second Kind Estimator (24, 25, 26)
+	- Special Function Definition Hankel Second Kind Estimator - Big H2 (27)
+	- Special Function Definition Hankel Second Kind Estimator - Evaluate (28)
+	- Special Function Definition Hankel Second Kind Estimator - Large Z Asymptote (29, 30)
+	- Special Function Definition Jacobi Estimator #1 (31, 32, 33)
+	- Special Function Definition Jacobi Estimator - n (34, 35)
+	- Special Function Definition Jacobi Estimator - Constructor (36, 37)
+	- Special Function Definition Jacobi Estimator - Alpha (38)
+	- Special Function Definition Jacobi Estimator - Beta (39)
+	- Special Function Definition Jacobi Estimator #2 (40)
+	- Special Function Definition Legendre Estimator (41, 42, 43)
+	- Special Function Definition Legendre Estimator - Constructor (44, 45)
+	- Special Function Definition Jacobi Estimator - Alpha (46)
+	- Special Function Definition Jacobi Estimator - Ceta (47)
+	- Special Function Definition Jacobi Estimator - Evaluate (48, 49)
+	- Special Function Definition Modified Bessel First Kind Estimator (50, 51, 52)
+	- Special Function Definition Modified Bessel First Kind Estimator - Alpha Positive Asymptote (53, 54, 55)
+	- Special Function Definition Modified Bessel First Kind Estimator - Big I (56)
+	- Special Function Definition Modified Bessel First Kind Estimator - Evaluate (57)
+	- Special Function Definition Modified Bessel Second Kind Estimator (58, 59, 60)
+
+
+Samples:
+
+IdeaDRIP:
diff --git a/ScheduleSheet.xlsx b/ScheduleSheet.xlsx
diff --git a/src/main/java/org/drip/specialfunction/definition/ConfluentHypergeometricEstimator.java b/src/main/java/org/drip/specialfunction/definition/ConfluentHypergeometricEstimator.java
@@ -134,8 +134,8 @@ public abstract class ConfluentHypergeometricEstimator extends HypergeometricEst
 {
 
 	protected ConfluentHypergeometricEstimator (
-		final org.drip.specialfunction.definition.HypergeometricParameters hypergeometricParameters)
-		throws java.lang.Exception
+		final HypergeometricParameters hypergeometricParameters)
+		throws Exception
 	{
 		super (hypergeometricParameters);
 	}
@@ -154,10 +154,10 @@ protected ConfluentHypergeometricEstimator (
 	 *  
 	 * @return Confluent Hyper-geometric Value
 	 * 
-	 * @throws java.lang.Exception Thrown if the Inputs are Invalid
+	 * @throws Exception Thrown if the Inputs are Invalid
 	 */
 
 	public abstract double confluentHypergeometric (
 		final double z)
-		throws java.lang.Exception;
+		throws Exception;
 }
diff --git a/src/main/java/org/drip/specialfunction/definition/EllipticEIntegralEstimator.java b/src/main/java/org/drip/specialfunction/definition/EllipticEIntegralEstimator.java
@@ -6,6 +6,9 @@
  */
 
 /*!
+ * 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 +81,7 @@
 
 /**
  * <i>EllipticEIntegralEstimator</i> exposes the Stubs for estimating the Elliptic E-Integral and its
- * Jacobian using the 2F1 Hyper-geometric Function. The References are:
+ * 	Jacobian using the 2F1 Hyper-geometric Function. The References are:
  * 
  * <br><br>
  * 	<ul>
@@ -103,37 +106,42 @@
  * 			Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_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/definition/README.md">Definition of Special Function Estimators</a></li>
+ * 		<li>Evaluate The Elliptic E Integral Function</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/ProductCore.md">Product Core Module</a></td></tr>
+ *		<tr><td><b>Library</b></td> <td><a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</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/definition/README.md">Definition of Special Function Estimators</a></td></tr>
+ *  </table>
+ *
  * @author Lakshmi Krishnamurthy
  */
 
-public abstract class EllipticEIntegralEstimator extends
-	org.drip.specialfunction.definition.HypergeometricEstimator
+public abstract class EllipticEIntegralEstimator extends HypergeometricEstimator
 {
 
 	protected EllipticEIntegralEstimator()
-		throws java.lang.Exception
+		throws Exception
 	{
-		super (
-			new org.drip.specialfunction.definition.HypergeometricParameters (
-				-0.5,
-				 0.5,
-				 1.0
-			)
-		);
+		super (new HypergeometricParameters (-0.5, 0.5, 1.));
 	}
 
 	@Override public double evaluate (
 		final double k)
-		throws java.lang.Exception
+		throws Exception
 	{
 		return ellipticEIntegral (k);
 	}
@@ -145,10 +153,10 @@ protected EllipticEIntegralEstimator()
 	 *  
 	 * @return The Elliptic E Integral Function Value
 	 * 
-	 * @throws java.lang.Exception Thrown if the Inputs are Invalid
+	 * @throws Exception Thrown if the Inputs are Invalid
 	 */
 
 	public abstract double ellipticEIntegral (
 		final double k)
-		throws java.lang.Exception;
+		throws Exception;
 }
diff --git a/src/main/java/org/drip/specialfunction/definition/EllipticKIntegralEstimator.java b/src/main/java/org/drip/specialfunction/definition/EllipticKIntegralEstimator.java
@@ -6,6 +6,9 @@
  */
 
 /*!
+ * 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 +81,7 @@
 
 /**
  * <i>EllipticKIntegralEstimator</i> exposes the Stubs for estimating the Elliptic K-Integral and its
- * Jacobian using the 2F1 Hyper-geometric Function. The References are:
+ * 	Jacobian using the 2F1 Hyper-geometric Function. The References are:
  * 
  * <br><br>
  * 	<ul>
@@ -103,37 +106,42 @@
  * 			Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_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/definition/README.md">Definition of Special Function Estimators</a></li>
+ * 		<li>Evaluate The Elliptic K Integral Function</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/ProductCore.md">Product Core Module</a></td></tr>
+ *		<tr><td><b>Library</b></td> <td><a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</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/definition/README.md">Definition of Special Function Estimators</a></td></tr>
+ *  </table>
+ *
  * @author Lakshmi Krishnamurthy
  */
 
-public abstract class EllipticKIntegralEstimator extends
-	org.drip.specialfunction.definition.HypergeometricEstimator
+public abstract class EllipticKIntegralEstimator extends HypergeometricEstimator
 {
 
 	protected EllipticKIntegralEstimator()
-		throws java.lang.Exception
+		throws Exception
 	{
-		super (
-			new org.drip.specialfunction.definition.HypergeometricParameters (
-				0.5,
-				0.5,
-				1.0
-			)
-		);
+		super (new HypergeometricParameters (0.5, 0.5, 1.));
 	}
 
 	@Override public double evaluate (
 		final double k)
-		throws java.lang.Exception
+		throws Exception
 	{
 		return ellipticKIntegral (k);
 	}
@@ -145,10 +153,10 @@ protected EllipticKIntegralEstimator()
 	 *  
 	 * @return The Elliptic K Integral Function Value
 	 * 
-	 * @throws java.lang.Exception Thrown if the Inputs are Invalid
+	 * @throws Exception Thrown if the Inputs are Invalid
 	 */
 
 	public abstract double ellipticKIntegral (
 		final double k)
-		throws java.lang.Exception;
+		throws Exception;
 }
diff --git a/src/main/java/org/drip/specialfunction/definition/HankelFirstKindEstimator.java b/src/main/java/org/drip/specialfunction/definition/HankelFirstKindEstimator.java
@@ -1,11 +1,18 @@
 
 package org.drip.specialfunction.definition;
 
+import org.drip.function.definition.CartesianComplexNumber;
+import org.drip.function.definition.R2ToZ1;
+import org.drip.numerical.common.NumberUtil;
+
 /*
  * -*- 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>HankelFirstKindEstimator</i> exposes the Estimator for the Hankel Function of the First Kind. The
- * References are:
+ * 	References are:
  * 
  * <br><br>
  * 	<ul>
@@ -102,19 +109,32 @@
  * 			Wikipedia (2019): Bessel Function https://en.wikipedia.org/wiki/Bessel_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/definition/README.md">Definition of Special Function Estimators</a></li>
+ * 		<li>Construct the Large z Asymptotic Form of Hankel First Kind Estimator</li>
+ * 		<li>Evaluate Hankel Function First Kind H1 given Alpha and z</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/ProductCore.md">Product Core Module</a></td></tr>
+ *		<tr><td><b>Library</b></td> <td><a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</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/definition/README.md">Definition of Special Function Estimators</a></td></tr>
+ *  </table>
+ *
  * @author Lakshmi Krishnamurthy
  */
 
-public abstract class HankelFirstKindEstimator implements org.drip.function.definition.R2ToZ1
+public abstract class HankelFirstKindEstimator implements R2ToZ1
 {
 
 	/**
@@ -125,17 +145,15 @@ public abstract class HankelFirstKindEstimator implements org.drip.function.defi
 
 	public static final HankelFirstKindEstimator LargeZAsymptote()
 	{
-		return new HankelFirstKindEstimator()
-		{
-			@Override public org.drip.function.definition.CartesianComplexNumber bigH1 (
+		return new HankelFirstKindEstimator() {
+			@Override public CartesianComplexNumber bigH1 (
 				final double alpha,
 				final double z)
 			{
-				return !org.drip.numerical.common.NumberUtil.IsValid (alpha) ||
-					!org.drip.numerical.common.NumberUtil.IsValid (z) ? null :
-					org.drip.function.definition.CartesianComplexNumber.FromPolar (
-						java.lang.Math.sqrt (2. / java.lang.Math.PI / z),
-						z - 0.5 * java.lang.Math.PI * alpha - 0.25 * java.lang.Math.PI
+				return !NumberUtil.IsValid (alpha) || !NumberUtil.IsValid (z) ? null :
+					CartesianComplexNumber.FromPolar (
+						Math.sqrt (2. / Math.PI / z),
+						z - 0.5 * Math.PI * alpha - 0.25 * Math.PI
 					);
 			}
 		};
@@ -150,17 +168,15 @@ public static final HankelFirstKindEstimator LargeZAsymptote()
 	 * @return Hankel Function First Kind H1 Value
 	 */
 
-	public abstract org.drip.function.definition.CartesianComplexNumber bigH1 (
+	public abstract CartesianComplexNumber bigH1 (
 		final double alpha,
-		final double z);
+		final double z
+	);
 
-	@Override public org.drip.function.definition.CartesianComplexNumber evaluate (
+	@Override public CartesianComplexNumber evaluate (
 		final double alpha,
 		final double z)
 	{
-		return bigH1 (
-			alpha,
-			z
-		);
+		return bigH1 (alpha, z);
 	}
 }