Package org.drip.numerical.estimation

Class R1ToR1SeriesTerm

java.lang.Object
org.drip.numerical.estimation.R1ToR1SeriesTerm
Direct Known Subclasses:
ASeriesTerm, GeneralizedMacLaurinSeriesTerm, MacLaurinSeriesTerm, PochhammerSeriesTerm, RelaxationTimeDistributionSeriesTerm
public abstract class R1ToR1SeriesTerm
extends java.lang.Object
R1ToR1SeriesTerm exposes the R1 To R1 Series Expansion Term in the Ordered Series of the Numerical Estimate for a Function. The References are:

  • Mortici, C. (2011): Improved Asymptotic Formulas for the Gamma Function Computers and Mathematics with Applications 61 (11) 3364-3369
  • National Institute of Standards and Technology (2018): NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/5.11
  • Nemes, G. (2010): On the Coefficients of the Asymptotic Expansion of n! https://arxiv.org/abs/1003.2907 arXiv
  • Toth V. T. (2016): Programmable Calculators – The Gamma Function http://www.rskey.org/CMS/index.php/the-library/11
  • Wikipedia (2019): Stirling's Approximation https://en.wikipedia.org/wiki/Stirling%27s_approximation


Author:
Lakshmi Krishnamurthy

  • Method Summary

    Modifier and Type Method Description
    static R1ToR1SeriesTerm Asymptotic()
    Construct the Asymptotic Series Expansion Term
    double derivative​(int order, int derivativeOrder, double x)
    Compute the Derivative of the R1 To R1 Series Expansion Term
    static R1ToR1SeriesTerm InvertedRisingExponential()
    Construct the Inverted Rising Exponential Series Expansion Term
    static R1ToR1SeriesTerm Taylor()
    Construct the Taylor Series Expansion Term
    abstract double value​(int order, double x)
    Compute the Value of the R1 To R1 Series Expansion Term

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • Asymptotic

      public static final R1ToR1SeriesTerm Asymptotic()
      Construct the Asymptotic Series Expansion Term
      Returns:
      The Asymptotic Series Expansion Term

    • InvertedRisingExponential

      public static final R1ToR1SeriesTerm InvertedRisingExponential()
      Construct the Inverted Rising Exponential Series Expansion Term
      Returns:
      The Inverted Rising Exponential Series Expansion Term

    • Taylor

      public static final R1ToR1SeriesTerm Taylor()
      Construct the Taylor Series Expansion Term
      Returns:
      The Taylor Series Expansion Term

    • value

      public abstract double value​(int order, double x) throws java.lang.Exception
      Compute the Value of the R1 To R1 Series Expansion Term
      Parameters:
      order - Order of the R1 To R1 Series Expansion Term
      x - X
      Returns:
      The Value of the R1 To R1 Series Expansion Term
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • derivative

      public double derivative​(int order, int derivativeOrder, double x) throws java.lang.Exception
      Compute the Derivative of the R1 To R1 Series Expansion Term
      Parameters:
      order - Order of the R1 To R1 Series Expansion Term
      derivativeOrder - Order of the R1 To R1 Series Derivative
      x - X
      Returns:
      The Derivative of the R1 To R1 Series Expansion Term
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid